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Mathematical concept
In mathematics, the coclass of a finite p-group of order pn is n − c where c is the nilpotency class. The coclass conjectures were introduced by Leedham-Green
Coclass
Software component technology from Microsoft
The following IDL code declares a coclass named SomeClass which implements an interface named ISomeInterface. coclass SomeClass { [default] interface ISomeInterface;
Component_Object_Model
c} and the coclass r = n − c {\displaystyle r=n-c} . It turned out that descendant trees of a particular kind, the so-called pruned coclass trees whose
Descendant tree (group theory)
Descendant_tree_(group_theory)
pro-p groups of coclass r. This finiteness result is fundamental for the classification of finite p-groups by means of directed coclass graphs. The canonical
Pro-p_group
Group in which the order of every element is a power of p
p-groups by their coclass, that is, the difference between their composition length and their nilpotency class. The so-called coclass conjectures described
P-group
not coclass settled, whence its entire descendant tree T ( R ) {\displaystyle {\mathcal {T}}(R)} is of considerably higher complexity than the coclass- 2
Artin_transfer_(group_theory)
Finite group
class n − 1 were the beginning of the classification of all p-groups via coclass. The modular maximal-cyclic group of order 2n always has nilpotency class
Quasidihedral_group
problem (Vaughan-Lee 1993), the classification of finite p-groups via the coclass conjectures (Leedham-Green & McKay 2002), and provided an excellent method
Powerful_p-group
descendant trees. The group ⟨ 27 , 3 ⟩ {\displaystyle \langle 27,3\rangle } of coclass 1 {\displaystyle 1} has ranks ν = 2 {\displaystyle \nu =2} , μ = 4 {\displaystyle
P-group_generation_algorithm
Israeli mathematician and writer
extensively in p-groups and pro-p groups and was among those who solved the coclass conjectures on the structure of such groups. Likewise Shalev used Lie methods
Aner_Shalev
Concept in mathematics
introduced by Avinoam Mann. These groups were critical for the proof of the coclass conjectures which introduced an important way to understand the structure
Omega_and_agemo_subgroup
German mathematician (born 1968)
contributor to the "coclass project" that aims to classify groups of prime power order and other nilpotent algebraic objects using coclass as a primary invariant
Bettina_Eick
History of a branch of mathematics
important. Many conjectures were made during this time, including the coclass conjectures. The last twenty years of the 20th century enjoyed the successes
History_of_group_theory
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