[PDF] Top 20 Conjugacy classes and graphs of two-groups of nilpotency class two
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Conjugacy classes and graphs of two-groups of nilpotency class two
... Conjugacy classes have already been there since the turn of the ...of conjugacy classes for 2-generator p-groups of class two (p an odd ...commuting conjugacy ... See full document
24
Point groups of order at most eight and their conjugacy class graphs
... called conjugacy class graph. In order to obtain the conjugacy class graph, the concept of conjugacy class is ...theory, conjugacy class is a method of partitioning ... See full document
29
Some problems about products of conjugacy classes in finite groups
... All cases of Theorem 4.2 are possible and examples of each of them are given in [4]. The techniques for proving Theorem 4.2 are relatively elementary although Glauberman’s Z ∗ theorem [10] and a result of Y. Berkovich ... See full document
10
Irreducible representation of finite metacyclic group of nilpotency class two of order 16
... Certain classes of metacyclic groups have been given much emphasis by many ...of class at least 3 where p is ...metacyclic groups has not been done ...metacyclic groups of class ... See full document
18
Commutativity degrees and related invariants of some finite nilpotent groups
... of two-generator p- groups of nilpotency class ...these groups for p is an odd prime and p 2, ...of conjugacy classes by the order of the ...of conjugacy ... See full document
23
Some numerical results on two classes of finite groups
... Polkouei, Some numerical results on finite non-abelian 2- generator p-groups of nilpotency class two , Annals Math Iasi, preprinted.. Sarmin, On some problems in group theory of probabil[r] ... See full document
10
Statistics in conjugacy classes in free groups
... the conjugacy class of x, so we may write (C) and C ...homotopy class determined by C ...non-trivial conjugacy classes C ...has two closed paths whose lengths have irrational ... See full document
15
Asymptotics in conjugacy classes for free groups
... in conjugacy classes; however, Parkkonen and Paulin considered orbit counting in conjugacy classes in the setting of variable negative ...in conjugacy classes in the setting of ... See full document
105
Orbit counting in conjugacy classes for free groups acting on trees
... Since the first version of this paper was written, we learned that Broise-Alamichel, Parkkonen and Paulin also have results for graphs and metric graphs which include Theorem 1.1 and the result of Douma. ... See full document
14
Some applications of Two-Generator p-Groups of Nilpotency class two
... capable groups which are direct sums of cyclic ...their two highest torsion coefficients ...other classes of groups, concentrating to some extent on nilpotent group of class ... See full document
11
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... nilpotent groups that have been classified. In this research, 2-generator p- groups of nilpotency class 2 (p an odd prime) are ...These groups were classified by Bacon and Kappe in 1993 ... See full document
17
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... Let G be a finite group and x, y ∈ G. If x and y are conjugate, then x and y have the same order. If x is conjugate to y, there exist g ∈ G such that g −1 xg = y. Now, xg = gy. Thus |xg| = |gy|. Hence |x| = |y|. The ... See full document
16
Infinite two generator groups of class two and their non abelian tensor squares
... 2-generator groups of nilpotency class two and the determination of their non-abelian tensor ...of class two, for p an odd prime or p = 2, ...generator groups of ... See full document
11
One-prime power hypothesis for conjugacy class sizes
... of conjugacy class sizes of G is an ongoing line of research, see [4] for an ...of conjugacy class sizes is encoded varies, but one representation is via the bipartite graph ... See full document
7
Bipartite divisor graph for the set of irreducible character degrees
... F (H)], [H : F (H)] } . As ∆(H) has two connected components, we can see that H is either a group of type one or four in the sense of [8]. Also by [17, Lemma 5.1] we deduce that m = [G : F (G)] and cd(F (G)) = {1, ... See full document
11
The conjugacy classes of metabelian groups of order at most 24
... non-central conjugacy classes. Moreover, the metabelian groups of types (9), (10) and 12) have the same number of non-central conjugacy classes of order greater than one, namely 5, and ... See full document
5
Automorphism groups of metacyclic groups of class two
... automorphism groups of metacyclic groups of class ...automorphism groups of metacyclic groups of class two have not been found by any ...of groups of class ... See full document
17
nth-roots and n-centrality of finite 2-generator p-groups of nilpotency class 2
... In this section, we again consider all finite non-abelian 2-generator p-groups (p 6= 2) of nilpotency class two and this time we investigate n-centrality for them.. Theorem 3.1.[r] ... See full document
11
CH-groups which are finite $p$-groups
... We conclude the paper by a remark on CH-p-and CA -groups. In [2], the authors provide examples showing that CA ⊂ CH .It might therefore be interesting to note that, if G is a CH-p-group and not of class 2 ... See full document
15
A note on maximal length elements in conjugacy classes of finite coxeter groups
... The maximal lengths of elements in each of the conjugacy classes of Coxeter groups of types B n , D n and E 6 are determined. Additionally, representative elements are given that attain these maximal ... See full document
10
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