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Finite group
mathematics, a normal p-complement of a finite group for a prime p is a normal subgroup of order coprime to p and index a power of p. In other words
Normal_p-complement
symmetrical: if K is a complement of H, then H is a complement of K. Neither H nor K need be a normal subgroup of G. Complements need not exist, and if
Complement_(group_theory)
Any of certain special normal subgroups of a group
every p-soluble group is p-constrained. A group is p-nilpotent if and only if it has a normal p-complement, which is just its p′-core. Just as normal cores
Core_(group_theory)
Tool in linear algebra and matrix analysis
so that M is a (p + q) × (p + q) matrix. If D is invertible, then the Schur complement of the block D of the matrix M is the p × p matrix defined by
Schur_complement
as the exponent of p increases. Most groups of small order have a Sylow p subgroup P with a normal p-complement N for some prime p dividing the order
List_of_small_groups
Automorphism group of the Klein quartic
its Sylow 2-subgroup provide a counter-example for various normal p-complement theorems for p = 2. G = PSL(2, 7) acts via linear fractional transformation
PSL(2,7)
Binary representation for signed numbers
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point
Two's_complement
Concept in mathematics
X is called a Frobenius complement. The identity element together with all elements not in any conjugate of H form a normal subgroup called the Frobenius
Frobenius_group
Part of the immune system that enhances the ability of antibodies and phagocytic cells
The complement system, also known as complement cascade, is a part of the humoral, innate immune system and enhances (complements) the ability of antibodies
Complement_system
Probability distribution
\left({\frac {a-\mu }{\sigma {\sqrt {2}}}}\right)\right]} The complement of the standard normal cumulative distribution function, Q ( x ) = 1 − Φ ( x ) {\textstyle
Normal_distribution
(on a complex Hilbert space) continuous linear operator
Eigenvectors of a normal operator corresponding to different eigenvalues are orthogonal, and a normal operator stabilizes the orthogonal complement of each of
Normal_operator
German mathematician (1849–1917)
145–146. ISBN 0-8218-1967-4. Theorem 9.4.1., p. 145, at Google Books Thompson, J.G. (1959). "Normal p-complements for finite groups". Mathematische Zeitschrift
Ferdinand_Georg_Frobenius
Method of subtraction
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they
Method_of_complements
Medical condition
Complement deficiency is an immunodeficiency of absent or suboptimal functioning of one of the complement system proteins. Because of redundancies in
Complement_deficiency
Graph with same nodes as but complementary connections to another
graph and let P consist of all pairs of distinct vertices in V. Then the simple undirected graph H = (V, P \ E) is the complement of G, where P \ E is the
Complement_graph
English mathematician
representations, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of Ferdinand Georg Frobenius
William_Burnside
Theorem in group theory
of the theorem is that any normal Hall subgroup N {\displaystyle N} of a finite group G {\displaystyle G} has a complement in G {\displaystyle G} . Moreover
Schur–Zassenhaus_theorem
Thompson subgroup and denoted by J ( P ) {\displaystyle J(P)} . Glauberman normal p-complement theorem ZJ theorem Puig subgroup, a subgroup analogous to
Thompson_subgroup
American mathematician (born 1941)
University Press, ISBN 978-0-521-45716-3, MR 1311244 Glauberman normal p-complement theorem Curriculum vitae, retrieved 2013-07-21. George Glauberman
George_Glauberman
Logical operation
logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition "not P {\displaystyle P} ", written ¬ P {\displaystyle
Negation
Standard forms of Boolean functions
be expressed in the canonical disjunctive normal form (CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms
Canonical_normal_form
Number with all digits equally frequent
the complement of X has measure 0. If x is normal in base b, and a ≠ 0 is a rational number, then x ⋅ a {\displaystyle x\cdot a} is also normal in base
Normal_number
Bound lattice in which every element has a complement
theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element
Complemented_lattice
closed set C and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from
Moore_space_(topology)
Opposite of a probability event
probability theory, the complement of any event A is the event [not A], i.e. the event that A does not occur. The event A and its complement [not A] are mutually
Complementary_event
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution
Multivariate normal distribution
Multivariate_normal_distribution
{\displaystyle \complement _{A}B=A\setminus B} . 2. Without a subscript, denotes the absolute complement; that is, ∁ A = ∁ U A {\displaystyle \complement A=\complement
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Broadway musical
production numbers" had been replaced by songs that complemented the emotional content of the book. Next to Normal began previews on Broadway at the Booth Theatre
Next_to_Normal
Generalization of perpendicularity
{\displaystyle V} that is orthogonal to a given subspace is its orthogonal complement. Given a module M {\displaystyle M} and its dual M ∗ {\displaystyle M^{*}}
Orthogonality_(mathematics)
Part of the innate immune system
C3b is the larger of two elements formed by the cleavage of complement component 3, and is considered an important part of the innate immune system. C3b
C3b
Complement control proteins are proteins that interact with components of the complement system. The complement system is tightly regulated by a network
Complement_control_protein
Shorthand used in statistics
68–95–99.7 rule, also known as the empirical rule or 68–95–99.7 rule for a normal distribution and sometimes abbreviated 3sr or 3 σ, is a shorthand used to
68–95–99.7_rule
In mathematical logic, an atomic formula or its negation
In the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula. In Boolean functions
Literal_(mathematical_logic)
Protein found in humans
Complement receptor type 2 (CR2), also known as complement C3d receptor, Epstein–Barr virus receptor, and CD21 (cluster of differentiation 21), is a protein
Complement_receptor_2
Probability distribution
calculated by its complement as f ( k , n , p ) = f ( n − k , n , 1 − p ) . {\displaystyle f(k,n,p)=f(n-k,n,1-p).} Looking at the expression f(k, n, p) as a function
Binomial_distribution
Protein-coding gene in the species Homo sapiens
encoded by the CFP (complement factor properdin) gene. Properdin and factor H are regulatory proteins in the alternative complement pathway. Properdin
Properdin
Typographical symbol (™)
preceding mark is a trademark, specifically an unregistered trademark. It complements the registered trademark symbol ® which is reserved for trademarks registered
Trademark_symbol
On solvability of Diophantine equations
equations p 1 = 0 , … , p k = 0 {\displaystyle p_{1}=0,\ldots ,p_{k}=0} (where each p i {\displaystyle p_{i}} is a polynomial) as a single equation p 1 2 +
Hilbert's_tenth_problem
Presence of an abnormal number of chromosomes in a cell
attached to both mitotic spindle poles. One daughter cell would have a normal complement of chromosomes; the second would lack one. A third daughter cell may
Aneuploidy
Destroyer of the Royal Navy
establishment at Plymouth, but did not stay long and was reduced to Reduced Complement on 5 March 1919. The Royal Navy was rationalising its destroyer force
HMS_Sharpshooter_(1917)
{\displaystyle X} is regular, completely regular, normal and completely normal. X / P {\displaystyle X/P} is the discrete topology. List of topologies –
Partition_topology
Medical condition
instigates activation of the entire complement pathway. Consequently, levels of all complement proteins become low. The complement pathway is composed of several
Urticarial_vasculitis
Angle in geometric optics
tangent, rather than that between the beam and the surface normal. The 90-degree complement to the angle of incidence is called the grazing angle or glancing
Angle_of_incidence_(optics)
Immunity strategy in living beings
chemical factors, including chemical mediators called cytokines activate the complement cascade to identify bacteria, activate cells, and promote clearance of
Innate_immune_system
Pair of logical equivalences
"not A and not B". or The complement of the union of two sets is the same as the intersection of their complements The complement of the intersection of
De_Morgan's_laws
Function of the observed sample results
hypothesis tests and p-values, and their connection to replicability. It states that "Different measures of uncertainty can complement one another; no single
P-value
Concept in mathematics
submanifold. Define, for a given p ∈ S {\displaystyle p\in S} , a vector n ∈ T p M {\displaystyle n\in \mathrm {T} _{p}M} to be normal to S {\displaystyle S} whenever
Normal_bundle
Reduced oxygen-carrying ability of the blood due to breakdown of red blood cells
acquired, potentially life-threatening disease of the blood characterized by complement-induced intravascular hemolytic anemia. Lead poisoning resulting from
Hemolytic_anemia
Destroyer of the Royal Navy
the vessel was carrying between 30 and 50 depth charges. The ship had a complement of 82 officers and ratings. Thruster was laid down by Hawthorn Leslie
HMS_Thruster_(1917)
British battleship
Coronation - Naval Review". The Times. No. 36845. London. 13 August 1902. p. 4. Brown, David K. (1997). Warrior to Dreadnought: Warship Development 1860–1905
HMS_Trafalgar_(1887)
American WWII-era fighter aircraft
Designer, Edgar Schmued and the P-51, p. 61. The comparison was between wind-tunnel tests of full-scale models, with normal heating (thermic engine) and
North_American_P-51_Mustang
Disease characterized by rapid swelling
angioedema, bradykinin formation is caused by continuous activation of the complement system due to a deficiency in one of its prime inhibitors, C1-esterase
Angioedema
American mathematician (1946–2012)
figure-eight knot complement. By utilizing Haken's normal surface techniques, he classified the incompressible surfaces in the knot complement. Together with
William_Thurston
Country in North America
Buchwald, M. (1992). "Cloning of cDNAs for Fanconi's anemia by functional complementation". Nature. 356 (6372): 763–767. doi:10.1038/356763a0. PMID 1574115.
Canada
Chicago "L" station
featuring large amounts of steel and glass and very little amenities, to complement the design of the brand new stainless-steel 2200 series trains that ran
69th_station
Maritime patrol and anti-submarine aircraft family
the type. In U.S. Navy service, the normal crew complement was 12 until it was reduced to its current complement of 11 in the early 2000s when the in-flight
Lockheed_P-3_Orion
Genetic disease causing anemia, birth defects, and cancers
Fanconi anemia has improved scientific understanding of the mechanisms of normal bone marrow function and the development of cancer. Among those affected
Fanconi_anemia
Mammalian protein found in humans
or dying cells (and some types of bacteria) in order to activate the complement system via C1q. CRP is synthesized by the liver in response to factors
C-reactive_protein
Number of sets of chromosomes of a cell
chromosomes within each of the 23 homologous pairs, providing a full complement of 46 chromosomes. This total number of individual chromosomes (counting
Ploidy
Set whose pairs have minima and maxima
bounded lattice for which every element has a complement is called a complemented lattice. A complemented lattice that is also distributive is a Boolean
Lattice_(order)
American mass murderer (1941–1991)
; Strong, J. A.; Whatmore, P. B.; McClemont, W. F. (March 12, 1966). "Criminal patients with XYY sex-chromosome complement". Lancet. 287 (7437): 565–6
Richard_Speck
Subgroup of a group in mathematics
retracts: A subgroup is a retract if and only if it has a normal complement. The normal complement, specifically, is the kernel of the retraction. Every direct
Retract_(group_theory)
Concept in probability theory
given a likelihood function p ( x ∣ θ ) {\displaystyle p(x\mid \theta )} , the posterior distribution p ( θ ∣ x ) {\displaystyle p(\theta \mid x)} is in the
Conjugate_prior
Class of enzymes
proactivator convertase, properdin factor D esterase, factor D (complement), complement factor D, CFD, adipsin) is a protein which in humans is encoded
Factor_D
Protein found in humans
Complement receptor type 1 (CR1) also known as C3b/C4b receptor or CD35 (cluster of differentiation 35) is a protein that in humans is encoded by the CR1
Complement_receptor_1
Component of blood aiding in coagulation
aggregates (PLAs). These formations induce upregulated production of the complement receptor αmβ2 (Mac-1) integrin in neutrophils. Interaction with PLAs also
Platelet
Class of animals
Varanids, and a few other lizard species, employ buccal pumping as a complement to their normal "axial breathing". This allows the animals to completely fill
Reptile
Destroyer of the Royal Navy
Destroyer, p.126 The Admiralty, The Navy List (various editions 1919-20). Dittmar; Colledge. British Warships 1914–1919, Ian Allan Publishing, 1972, p. 71.
HMS_Radiant
Musical instrument
Giuliani and Caspar Joseph Mertz wrote extensively for the terz guitar as a complement to the prime (standard) guitar. Acceptable alternate spellings for terz
Six-string_alto_guitar
Countable intersection of open sets
sets { q } c {\displaystyle \{q\}^{c}} (the superscript denoting the complement) where q {\displaystyle q} is rational. The set of rational numbers Q
Gδ_set
Dietary theory for protein nutrition
Protein combining or protein complementing is a process in which individual plant products that by themselves are deficient in one or more essential amino
Protein_combining
any two Sylow systems are conjugate. Any normal Hall subgroup H of a finite group G possesses a complement, that is, there is some subgroup K of G that
Hall_subgroup
Genetic condition in which a male has an extra Y chromosome
risk of learning disabilities. Most individuals with this condition have normal fertility. The condition is generally not inherited but rather occurs as
XYY_syndrome
Multi-ship class of aircraft carrier
and the ships had a complete double bottom. In 1939, Courageous had a complement of 807 officers and ratings, plus 403 men in her air group. Their half-sister
Courageous-class aircraft carrier
Courageous-class_aircraft_carrier
Proposed parameter in linguistics
head-initial (the head of a phrase precedes its complements) or head-final (the head follows its complements). The head is the element that determines the
Head-directionality_parameter
Boolean polynomials as sums of monomials
Algebraic normal form (ANF) is a representation of functions in boolean algebra. Formulas written in ANF are also known as ring sum normal form (RSNF or
Algebraic_normal_form
Function returning one of only two values
arguments and their complements Conjunctive normal form, as an AND of ORs of the arguments and their complements Canonical normal form, a standardized
Boolean_function
Vision loss due to damage to the macula of the eye
Haines JL, Hauser MA, Schmidt S, Scott WK, Olson LM, Gallins P, et al. (April 2005). "Complement factor H variant increases the risk of age-related macular
Macular_degeneration
Number measuring the chance an event occurs
{\displaystyle {\overline {A}},A^{\complement },\neg A} , or ∼ A {\displaystyle {\sim }A} ; its probability is given by P(not A) = 1 − P(A). As an example, the chance
Probability
Autoimmune disease in which the immune system attacks healthy tissue
RNASEH2C, Complement component 1qA, Complement component 1qB, Complement component 1r, Complement component 1s, Complement component 2, Complement component
Lupus
Immune organ that filters blood
bacteria. Encapsulated bacteria inhibit the binding of complement or prevent the complement assembled on the capsule from interacting with macrophage
Spleen
Life-threatening immune-related blood disease
Atypical hemolytic uremic syndrome (aHUS), also known as complement-mediated hemolytic uremic syndrome (not to be confused with hemolytic–uremic syndrome)
Atypical hemolytic uremic syndrome
Atypical_hemolytic_uremic_syndrome
Military unit
machine guns went down to 20% of normal complement, and mortars with infantry support guns were down to 10% of normal complement. List of Japanese Infantry
24th Division (Imperial Japanese Army)
24th_Division_(Imperial_Japanese_Army)
Unique knot with a crossing number of four
Thurston showed that the figure-eight was hyperbolic, by decomposing its complement into two ideal hyperbolic tetrahedra. (Robert Riley and Troels Jørgensen
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Protein-coding gene in the species Homo sapiens
recognition immune clearance, SAP binds in a calcium dependent manner to complement component C1q and the antibody binding region of immunoglobulins (Fab)
Serum_amyloid_P_component
British M-Class destroyer
consisted of two twin mounts for 21 in (533 mm) torpedoes. The ship had a complement of 76 officers and ratings. Laid down by William Doxford & Sons of Sunderland
HMS_Oracle_(1915)
S class destroyer in WW II
miles (5,090 km; 3,160 mi) at 15 knots (28 km/h; 17 mph). The ship had a complement of 90 officers and ratings. Armament consisted of three QF 4-inch (102 mm)
HMS_Stronghold
Spanish football scandal
extended to technical reports related to professional refereeing in order to complement the information requested by the first and second team coaching staff"
Negreira_case
Species of snake
Anerythristic (anerythristic type A, sometimes called "Black Albino") – The complement to amelanism. The inherited recessive mutation of lacking erythrin (red
Corn_snake
Victor III-class submarine Displacement 4,950 tons light surfaced 6,990 tons normal surfaced 7,250 tons submerged Length 93–102 m (305 ft 1 in – 334 ft 8 in)
Russian submarine Daniil Moskovsky
Russian_submarine_Daniil_Moskovsky
Mathematical function characterizing set membership
the complement of A {\displaystyle A} i.e. A ∁ {\displaystyle A^{\complement }} is: 1 A ∁ = 1 − 1 A . {\displaystyle \mathbf {1} _{A^{\complement }}=1-\mathbf
Indicator_function
Country in South Asia
shalwar-kameez in Puducherry A typical Indian meal is built on a plain cereal, complemented by savoury dishes. The cooked cereal could be steamed rice; chapati,
India
2024 studio album by Taylor Swift
monotonous and "staid", but others argued that the minimalistic approach complemented Swift's hyper-personal lyrics; Hopper opined that "Swift's confidence
The_Tortured_Poets_Department
Data structure for Boolean functions
compactly, using complemented edges, also known as complement links. The resulting BDD is sometimes known as a typed BDD or signed BDD. Complemented edges are
Binary_decision_diagram
Class of proteins involved in inflammation
growth of microbes, e.g., C-reactive protein, mannose-binding protein, complement factors, ferritin, ceruloplasmin, serum amyloid A and haptoglobin. Others
Acute-phase_protein
two players to the same defensive position during a season, normally to complement a batter who hits well against left-handed pitchers with one who hits
Glossary_of_baseball_terms
Protein-coding gene in the species Homo sapiens
Complement C4-A is a kind of the Complement component 4 protein that in humans is encoded by the C4A gene. This gene encodes the acidic form of complement
C4A
1992 class of corvettes of the Royal Thai Navy
(28 km/h; 17 mph). The corvettes have a complement of 6 officers and 51 enlisted. The class is equipped with Plessey Nautis P combat data system and the British
Khamronsin-class_corvette
Thornycroft M-class destroyer of the Royal Navy
(2,850 km; 1,770 mi) at 15 knots (28 km/h; 17 mph). The vessel had a complement of 78 officers and ratings. Armament consisted of three QF 4-inch (102 mm)
HMS_Mastiff_(1914)
Group of genetic connective tissues disorders
are those that affect glycosaminoglycan biosynthesis. Defects in the complement pathway characterize Group E disorders. Group F are disorders of intracellular
Ehlers–Danlos_syndrome
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NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
NORMAL P-COMPLEMENT
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