conjugacy class
The conjugate graph and conjugacy class graph of order at most 32
... of conjugacy class graph of 𝐺 , α 𝐺 b) The chromatic number of conjugacy class graph of 𝐺 , 𝐺 c) The clique number of conjugacy class graph of 𝐺 , 𝐺 d) The dominating number of ...
9
One-prime power hypothesis for conjugacy class sizes
... As Taeri comments, B(G) having no cycle of length 4 is equivalent to G satisfying the one-prime power hypothesis, that is, if m and n are distinct non-trivial conjugacy class sizes of G then either m and n ...
7
Point groups of order at most eight and their conjugacy class graphs
... theory, conjugacy classes, point groups in chemistry with their symmetry operations and stereographic ...the conjugacy classes, and conjugacy class graph are included ...
29
Finite groups with the same conjugacy class sizes as a finite simple group
... Abstract. For a finite group H , let cs(H) denote the set of non-trivial conjugacy class sizes of H and OC(H) be the set of the order components of H . In this paper, we show that if S is a finite simple ...
11
On finite groups with square-free conjugacy class sizes
... to conjugacy class sizes of some elements of a group not divisible by p 2 , for some fixed prime ...square-free class sizes for all primes. Finally, in Section 4, the topic of conjugacy ...
8
Recognizing L2(p) by its order and one special conjugacy class size
... In the past thirty years, many authors investigated some quantitative characterizations of finite groups, especially finite simple groups, such as quantitative characterizations by group order and element orders, by the ...
10
On p regular G conjugacy class sizes
... In a recent paper [], the authors studied the structure of G under the condition that the largest two p-regular conjugacy class sizes (say, m and n) of G are coprime, where m > n and p n. Notice that, ...
9
The conjugacy class ranks of $M_{24}$
... to study the ranks of M 24 with respect to the conjugacy classes of all its nonidentity elements.. It is a 5-transitive permutation group on.[r] ...
6
Conjugacy classes contained in normal subgroups: an overview
... be noted that similar results have also been studied for other graphs. In [19], S. Dolfi defines the dual graph of Γ(G) whose vertices are the primes which occur as divisors of the class sizes of G, and two ...
14
Orbit counting in conjugacy classes for free groups acting on trees
... Abstract. In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. ...
14
The conjugacy classes of metabelian groups of order at most 24
... denotes conjugacy class of the element x in G. Conjugacy class is an equivalence relation and it partitions the group into disjoint equivalence classes or ...of conjugacy classes of ...
5
Some problems about products of conjugacy classes in finite groups
... conjugacy class. We find a normal subgroup of a group when there is a conjugacy class satisfying that some of its powers is again a conjugacy class, and obtain an equivalent ...
10
Statistics in conjugacy classes in free groups
... Then (x ) and x are positive and depend only on the conjugacy class of x, so we may write (C) and C . Furthermore, (C) is the length of the closed geodesic on the quotient \ X in the free homotopy ...
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 compact manifolds with ...
105
A note on maximal length elements in conjugacy classes of finite coxeter groups
... the conjugacy classes of finite Coxeter groups, and prin- cipally those of the irreducible finite Coxeter groups, has come from many directions, for example in the representation theory of these groups and the ...
10
Non-nilpotent groups with three conjugacy classes of non-normal subgroups
... two conjugacy class of non-normal subgroups of size p; and for the group (xiii), |H| = q or q 2 and in each case N contains just one class of non-normal subgroups of size ...
7
Conjugacy classes and graphs of two-groups of nilpotency class two
... the conjugacy classes on the structure of a finite group have been the subject of research over the ...the conjugacy class sizes depend on the order of the commutator ...
24
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... Let G be a finite group and x, y ∈ G. If x and y are conjugate, then x and y have the same order. Suppose x n = 1. Then y n = (x g ) n = (x n ) g = 1. Thus |x| = |y|. The conjugacy class containing the ...
17
Groups with reality and conjugacy conditions
... Abstract. Many results were proved on the structure of finite groups with some restrictions on their real elements and on their conjugacy classes. We generalize a few of these to some classes of infinite groups. ...
14
Conjugacy in relatively extra-large Artin groups
... consider conjugacy of elements and parabolic subgroups in details, in a new class of Artin groups, introduced in an earlier work, which may contain arbitrary parabolic ...a conjugacy class and ...
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