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On certain subgroups of a minimal simple finite group of odd order
In mathematical finite group theory, Thompson's original uniqueness theorem (Feit & Thompson 1963, theorems 24.5 and 25.2) states that in a minimal simple
Thompson_uniqueness_theorem
Index of articles associated with the same name
first-order differential equations. Thompson uniqueness theorem in finite group theory. Carlson's theorem, the uniqueness of certain analytic functions taking
Uniqueness_theorem
Classification theorem in group theory
In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved in the early 1960s
Feit–Thompson_theorem
American mathematician
formula Thompson subgroup Thompson transitivity theorem Thompson uniqueness theorem Thompson, John Griggs — serge.mehl.free.fr Liste des 122 fondations
John_G._Thompson
theory) Sylow theorems (group theory) Thompson transitivity theorem (finite groups) Thompson uniqueness theorem (finite groups) Tits alternative (geometric
List_of_theorems
Theorem classifying finite simple groups
odd prime (classified by the Gilman–Griess theorem and work by several others), and groups of uniqueness type, where a result of Aschbacher implies that
Classification of finite simple groups
Classification_of_finite_simple_groups
the proof of the odd order theorem by Feit and Thompson (1963), where it was used to prove the Thompson uniqueness theorem. Suppose that G is a finite
Thompson_transitivity_theorem
Mathematical group based upon a finite number of elements
order divisible by at least three distinct primes. The Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable
Finite_group
Sporadic simple group
cyclic group C2. Sims (1973) proved the existence of such a group and its uniqueness up to isomorphism with a combination of permutation group theory and machine
Lyons_group
Concept in Hilbert spaces mathematics
this theorem is due to K. Löwner who gave a necessary and sufficient condition for f to be operator monotone. An elementary proof of the theorem is discussed
Trace_inequality
2G2(32n+1). (Here O(G) denotes the unique largest normal subgroup of G of odd order.) The original statement of Walter's theorem did not quite identify the Ree
Walter_theorem
a system of ordinary differential equations: the usual theorems on the existence and uniqueness of solutions to ordinary differential equations imply that
Inverse problem for Lagrangian mechanics
Inverse_problem_for_Lagrangian_mechanics
of the nontrivial elements of an abelian group. The signalizer functor theorem provides the conditions under which the source of such a functor is in
Signalizer_functor
Monster and modular connection
Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized
Monstrous_moonshine
position. The normal form of a term, if one exists, is unique (as a corollary of the Church–Rosser theorem). However, a term may have more than one head normal
Beta_normal_form
Algebraic structure
and Walter (1964, p.169, 1965) in order to extend Thompson's uniqueness results in the odd order theorem to groups with dihedral Sylow 2-subgroups. There
P-stable_group
Finite group
{\displaystyle 2^{5}} . The uniqueness of such a nonsplit extension was shown by Dempwolff (1972), and the existence by Thompson (1976), who showed using
Dempwolff_group
becomes the unique minimizer. This follows from Ivanov's theorem since the Hausdorff area of a Finsler manifold is never less than the Holmes–Thompson area,
Filling_area_conjecture
Sporadic simple group
construction. Griess's construction showed that the monster exists. Thompson showed that its uniqueness (as a simple group satisfying certain conditions coming from
Monster_group
Group without normal subgroups other than the trivial group and itself
while the remaining 6 are referred to as pariahs. The famous theorem of Feit and Thompson states that every group of odd order is solvable. Therefore,
Simple_group
Mathematical optimization concept
two optima are equal. These theorems belong to a larger class of duality theorems in optimization. The strong duality theorem is one of the cases in which
Dual_linear_program
Interpretation of probability
sequential use of Bayes' theorem: as more data become available, calculate the posterior distribution using Bayes' theorem; subsequently, the posterior
Bayesian_probability
quotes as of August 2026[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic
List_of_conjectures
Concept in mathematics
called the Frobenius kernel K. (This is a theorem due to Frobenius (1901); there is still no proof of this theorem that does not use character theory, although
Frobenius_group
Alfred Tarski (1961, Theorem 5). Smirnov (1971), named them after Georg Cantor because of Cantor's pairing function and Cantor's theorem that an infinite
Jónsson–Tarski_algebra
Type of metric geometry
x_{i}+\Delta y_{i}=\Delta x_{i}+|f(x_{i})-f(x_{i-1})|.} By the mean value theorem, there exists some point x i ∗ {\displaystyle x_{i}^{*}} between x i {\displaystyle
Taxicab_geometry
American columnist, author and lecturer (born 1946)
Last Theorem, Savant published the book The World's Most Famous Math Problem (October 1993), which surveys the history of Fermat's Last Theorem as well
Marilyn_vos_Savant
Sporadic simple group
(Gorenstein 1993) Leon, Jeffrey S.; Sims, Charles C. (1977). "The existence and uniqueness of a simple group generated by {3,4}-transpositions". Bull. Amer. Math
Baby_monster_group
Cauchy–Kovalevskaya theorem In mathematics, the Cauchy–Kowalevski theorem (also written as the Cauchy–Kovalevskaya theorem) is the main local existence and uniqueness theorem
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
exist. A p-complement is a complement to a Sylow p-subgroup. Theorems of Frobenius and Thompson describe when a group has a normal p-complement. Philip Hall
Complement_(group_theory)
German mathematician (1849–1917)
forms a subgroup which is nilpotent as John G. Thompson showed in 1959. All known proofs of that theorem make use of characters. In his first paper about
Ferdinand_Georg_Frobenius
Type of differential equation
Springer Science+Business Media. doi:10.1007/978-0-387-74372-1. ISBN 978-0387743714. Skip Thompson (ed.). "Delay-Differential Equations". Scholarpedia.
Delay_differential_equation
Maximum attainable efficiency of any heat engine
Carnot's theorem (English: /kɑːrˈnoʊ/ kar-NOH, French: [kaʁno]), also called Carnot's rule or Carnot's law, is a principle of thermodynamics developed
Carnot's theorem (thermodynamics)
Carnot's_theorem_(thermodynamics)
Theorem in algebraic geometry
In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact
Hurwitz's automorphisms theorem
Hurwitz's_automorphisms_theorem
Probability of shared birthdays
Birthday Problem, Ramanujan Journal, 2012, [1]. Brink 2012, Theorem 2 Brink 2012, Theorem 3 Brink 2012, Table 3, Conjecture 1 "Minimal number of people
Birthday_problem
Probability distribution
23: 21–25. doi:10.1016/0167-7152(94)00090-U. Nowakowski, Sz. (2021). "Uniqueness of a Median of a Binomial Distribution with Rational Probability". Advances
Binomial_distribution
Concept in normed space geometry
In geometry of normed spaces, the Holmes–Thompson volume is a notion of volume that allows to compare sets contained in different normed spaces (of the
Holmes–Thompson_volume
Italian mathematician (born 1940)
"asymptotic sieve". In 1980, he supplied the completion of the proof of the uniqueness of finite groups of Ree type in characteristic 3; at the time of its publication
Enrico_Bombieri
Group in which the order of every element is a power of p
exert control over the group that was used in the proof of the Feit–Thompson theorem. Certain central extensions of elementary abelian groups called extraspecial
P-group
Mathematical concept
Example 7.24 Wolf 1998, p. 208, Theorem 7.2 Smith, Eggen & St. Andre 2006, pg. 141 Theorem 3.3(a) Lay 2006, p. 71, Theorem 7.26 Briggs & Cochran 2011, pp
Inverse_function
Physical law for entropy and heat
proper definition of entropy and was based on caloric theory, is Carnot's theorem, formulated by the French scientist Sadi Carnot, who in 1824 showed that
Second_law_of_thermodynamics
Chinese-American mathematician (born 1949)
partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors
Shing-Tung_Yau
usual theorems from the integration theory of functions to the integration of correspondences, such as Lebesgue's Dominated convergence theorem. It uses
Integral_of_a_correspondence
American-born British filmmaker (born 1940)
Zero Theorem: Terry Gilliam's Latest!". Empire. 13 August 2012. Eisenberg, Eric (2012). "Christoph Waltz to Star in Terry Gilliam's Zero Theorem". Cinema
Terry_Gilliam
Hypothetical physical concept
Gödel's incompleteness theorem suggests that attempts to construct a theory of everything are bound to fail. Gödel's theorem, informally stated, asserts
Theory_of_everything
Set with associative invertible operation
{\displaystyle b} is unique; it is called the inverse of a {\displaystyle a} and is commonly denoted a − 1 {\displaystyle a^{-1}} . Note: Uniqueness of the identity
Group_(mathematics)
Observational basis of thermodynamics
now known as the first and second laws were established. Later, Nernst's theorem (or Nernst's postulate), which is now known as the third law, was formulated
Laws_of_thermodynamics
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
its boundary being its extrema, then the divergence theorem reduces to the fundamental theorem of calculus: ∫ x m x m + 1 F ( x ′ ) d x ′ = 0 , {\displaystyle
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Field of knowledge
verification and allows formal proof of difficult theorems of mathematics such as the Feit–Thompson theorem on finite groups. Algorithmics, a large part of
Mathematics
Number, approximately 3.14
analysis is ultimately a consequence of the Stone–von Neumann theorem, asserting the uniqueness of the Schrödinger representation of the Heisenberg group
Pi
Statistical distribution for dependence between random variables
and minimize tail risk and portfolio-optimization applications. Sklar's theorem states that any multivariate joint distribution can be written in terms
Copula_(statistics)
Retrieved 2024-09-22. Aigner, Martin (2013). Markov's theorem and 100 years of the uniqueness conjecture. Cham: Springer. doi:10.1007/978-3-319-00888-2
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Arrangement of points on a sphere
work of Landkof. For non-integrable Riesz kernels, the poppy-seed bagel theorem holds, see the 2004 work of Hardin and Saff. Notable cases include: α = ∞
Thomson_problem
nilpotent group, by Malcev's theorem, but not groups like the metaplectic group. Some infinite groups are simple, such as the Thompson groups. An infinite group
Infinite_group
Branch of mathematics
nature of groups, with basic theorems such as the fundamental theorem of finite abelian groups and the Feit–Thompson theorem. The latter was a key early
Algebra
Hungarian and American mathematician and physicist (1903–1957)
economy, he proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem. Von Neumann's model of an expanding
John_von_Neumann
2000 off-Broadway musical
Tango is a 2000 off-Broadway musical about the proof of Fermat's Last Theorem, written by husband and wife Joshua Rosenblum (music, lyrics) and Joanne
Fermat's_Last_Tango
Type of group
The proof of this fact in infinite group theory relies upon the Feit–Thompson theorem on the solubility of finite groups of odd order (Robinson 1996, p. 432)
Locally_finite_group
Principle in genetics
Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will
Hardy–Weinberg_principle
Studies linear representations of finite groups over fields of positive characteristic
result on embedding of elements of order 2 in finite groups called the Z* theorem, proved by George Glauberman using the theory developed by Brauer, was
Modular_representation_theory
Property of being an even or odd number
in understanding the configuration space of these puzzles. The Feit–Thompson theorem states that a finite group is always solvable if its order is an odd
Parity_(mathematics)
Geometric space with eight dimensions
have the property that every non-zero vector has a unique multiplicative inverse. Hurwitz's theorem prohibits such a structure from existing in dimensions
Eight-dimensional_space
Type of random mathematical object
variable can be used to uniquely identify or characterize random variables and prove results like the central limit theorem. In the theory of point processes
Poisson_point_process
Matrix operation generalizing exponentiation of scalar numbers
and we have simply Z = X + Y. For Hermitian matrices there is a notable theorem related to the trace of matrix exponentials. If A and B are Hermitian matrices
Matrix_exponential
Infinite polyhedron with non-planar faces
curved into approximating infinite cylinders in 3-space. He wrote some theorems: For every regular polyhedron {p,q}: (p−2)*(q−2)<4. For Every regular tessellation:
Skew_apeirohedron
Sporadic simple group
points that are collinear. A Fano subplane likewise satisfies suitable uniqueness conditions. To W21 append 3 new points and let the automorphisms in PΓL(3
Mathieu_group_M24
Lower relative opportunity cost in producing a good
John C. (2016). "Testing the General Validity of the Heckscher-Ohlin Theorem". American Economic Journal: Microeconomics. 8 (4): 54–90. doi:10.1257/mic
Comparative_advantage
Instantaneous rate of change (mathematics)
constant, because the derivative of a constant is zero. The fundamental theorem of calculus shows that finding an antiderivative of a function gives a
Derivative
Probability concept
continuous-time Markov chains.) Let P {\displaystyle P} be the (unique) solution of the system (0). (Uniqueness guaranteed by our assumption that Q {\displaystyle
Continuous-time_Markov_chain
American mathematician (born 1956)
James Cannon. Among his earliest contributions is his theorem that the Gieseking manifold is the unique cusped hyperbolic 3-manifold of smallest volume. The
Colin_Adams_(mathematician)
Number of vectors in any basis of the vector space
space. An important result about dimensions is given by the rank–nullity theorem for linear maps. If F / K {\displaystyle F/K} is a field extension, then
Dimension_(vector_space)
Measure of temperature relative to absolute zero
available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same average energy
Thermodynamic_temperature
Physical law
equivalent way by expanding the vector triple product and applying Stokes' theorem: F 12 = − μ 0 4 π ∫ L 1 ∫ L 2 ( I 1 d ℓ 1 ⋅ I 2 d ℓ 2 ) r ^ 21 |
Ampère's_force_law
Extremely small quantity in calculus; thing so small that there is no way to measure it
known as the method of indivisibles in his work The Method of Mechanical Theorems to find areas of regions and volumes of solids. In his formal published
Infinitesimal
2025. Nordstrom, Leigh (26 January 2026). "Haley Lu Richardson Embraces Unique Collaboration in Sundance Film 'Zi'". WWD. Retrieved 13 February 2025. "The
List of film director and actor collaborations
List_of_film_director_and_actor_collaborations
Algebraic variety
better part of the 20th century. Manin–Drinfeld theorem Moduli stack of elliptic curves Modularity theorem Shimura variety, a generalization of modular curves
Modular_curve
the imaging process and the geometry of the cameras used (epipolar and uniqueness constraint), and on the other hand, to postulated properties of the observed
Correspondence_problem
Application of information theory to thermodynamics and statistical mechanics
scenarios, making the derivation of the entropy production fluctuation theorem straightforward. For non-equilibrium processes, as is so for macroscopic
Maximum entropy thermodynamics
Maximum_entropy_thermodynamics
Physical lower limit to energy consumption of computation
computation Extended mind thesis Maxwell's demon Koomey's law No-deleting theorem Charles H. Bennett (2003), "Notes on Landauer's principle, Reversible Computation
Landauer's_principle
whether computers could calculate such possibilities; Gödel's incompleteness theorems; in 1974 the Arecibo Ionospheric Observatory found the Hulse–Taylor binary
List_of_Equinox_episodes
Method to solve optimization problems
equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. Dantzig's work was made available
Linear_programming
From an exceptional automorphism of a Dynkin diagram
subgroups of the Ree groups are elementary abelian of order 8. Walter's theorem shows that the only other non-abelian finite simple groups with abelian
Ree_group
American mathematician
triangulated in an essentially unique way. In 1959, Bing published an independent proof of the triangulation theorem, which had recently been proved
R._H._Bing
Equation of the state of a hypothetical ideal gas
law, and the second line uses Hamilton's equations and the equipartition theorem. Summing over a system of N particles yields 3 N k B T = − ⟨ ∑ k = 1 N
Ideal_gas_law
Resource problem in machine learning
strategies in "some aspects of the sequential design of experiments". A theorem, the Gittins index, first published by John C. Gittins, gives an optimal
Multi-armed_bandit
Country in South Asia
BCE) contain the earliest extant verbal expression of the Pythagorean theorem (although very likely it had been known to the Old Babylonians.) All mathematical
India
Hexagonal lattice made of carbon atoms
the Dirac point. This level is a consequence of the Atiyah–Singer index theorem and is half-filled in neutral graphene, leading to the "+1/2" in the Hall
Graphene
2023 film by Christopher Nolan
Urbaniak as Kurt Gödel, an Austrian logician and mathematician known for his theorems that revolutionized mathematics and had far-reaching implications for philosophy
Oppenheimer_(film)
Thermodynamic cycle
engine. Apart from the features implemented to avoid Otto patents, the truly unique part of Atkinson's design is that the engines have an expansion stroke that
Atkinson_cycle
Atkinson–Stiglitz theorem Where the utility function is separable between labor and all commodities, no indirect taxes need be employed. Aumann's agreement theorem If
Glossary_of_economics
black hole due to quantum effects, torsion, or other phenomena? No-hair theorem: Do black holes have an internal structure? If so, how might the internal
List of unsolved problems in astronomy
List_of_unsolved_problems_in_astronomy
Interpretation of quantum mechanics
between the probability density and the wave function has the status of a theorem, a result of a separate postulate, the "quantum equilibrium hypothesis"
De_Broglie–Bohm_theory
Physics phenomenon
Greenberger, M. Horne, and A. Zeilinger, "Going beyond Bell's Theorem," in Bell's Theorem, Quantum Theory and Conceptions of the Universe, edited by M
Quantum_entanglement
Concepts from linear algebra
state of the system. The Perron–Frobenius theorem gives sufficient conditions for a Markov chain to have a unique dominant eigenvalue, which governs the
Eigenvalues_and_eigenvectors
Concept in mathematical group theory
classification of finite simple groups. Close to half of the proof of the Feit–Thompson theorem involves intricate calculations with character values. Easier, but
Character_theory
List of concepts in artificial intelligence
colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Functional programming language
relative of Haskell. Its biggest deviation from Haskell is in the use of uniqueness types instead of monads for input/output (I/O) and side effects. A series
Haskell
Specific mathematical differential form
d f ≠ δ u {\displaystyle \mathrm {d} f\neq \delta u} The fundamental theorem of calculus for line integrals requires path independence in order to express
Inexact_differential
In probability theory, a rule for assigning epistemic probabilities
parameterization the probability density will be uniform. Liouville's theorem justifies the use of canonically conjugate variables, such as positions
Principle_of_indifference
Global electromagnetic resonances, generated and excited by lightning discharges
63rd Meeting: 682. Jackson, J. D. (August 2008). "Examples of the zeroth theorem of the history of science" (PDF). American Journal of Physics. 76 (8):
Schumann_resonances
travel, tourism, insurance
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
Surname or Lastname
English (chiefly Midlands and northern England, especially Yorkshire)
English (chiefly Midlands and northern England, especially Yorkshire) : patronymic from Hann or the byname Hand.Irish : shortened Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).Irish : variant of McKittrick.Respelling of Scandinavian Hansen or Hansson.Jewish (Ashkenazic) : metronymic from the female personal name Hanna.A family by the name of Hanson were established in America by John Hanson, one of four brothers sent there by Queen Christina of Sweden in 1642. They were grandsons of an Englishman who had married into the Swedish royal family; he was descended from a certain Roger de Rastrick, who had lived in Yorkshire in the 13th century.
Surname or Lastname
English
English : patronymic from the personal name Henn(e), a short form of Henry 1, Hayne (see Hain 2), or Hendy.Irish : Anglicized form of Gaelic Ó hAmhsaigh (see Hampson 2).
Boy/Male
Australian, Biblical
Twin
Female
English
Abbreviated form of English Thomasina, THOMASIN means "twin."Â
Boy/Male
Arabic
Uniqueness of Religion
Surname or Lastname
English
English : variant of Tims.
Surname or Lastname
English
English : patronymic from Tom, a short form of the personal name Thomas.
Surname or Lastname
English (mainly Lancashire)
English (mainly Lancashire) : patronymic from the Norman personal name Hamo, Hamon (see Hammond).Irish : shortened Anglicized form of Gaelic Ó hAmhsaigh ‘descendant of Amhsach’ a byname meaning ‘mercenary soldier’ or ‘messenger’, from the adjective amhasach ‘aggressive’.
Surname or Lastname
English
English : patronymic from the personal name Thomas.
Boy/Male
Arabic
Rarity; Uniqueness
Boy/Male
English
Derives from Thomas 'Twin.
Surname or Lastname
English
English : patronymic from Thomas. Thompson is widely distributed throughout Britain, but is most common in northern England and northern Ireland.Americanized form of Thomsen.
Surname or Lastname
English
English : patronymic from Tom, a short form of the personal name Thomas.
Girl/Female
Australian, Christian, Hebrew
Twin
Boy/Male
Australian, Biblical, British, English, Hebrew
Twin; Derives from Thomas
Surname or Lastname
English
English : variant of Hobson.
Boy/Male
Scandinavian
Thunder.' Surname.
Girl/Female
Hindu, Indian, Traditional
Propounder of the Uniqueness of the Absolute
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
THOMPSON UNIQUENESS-THEOREM
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