Multiplicities of conjugacy class sizes of finite groups
نویسندگان
چکیده
منابع مشابه
COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS
Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
متن کاملThe structure of finite groups with three class sizes
Let G be a finite group and suppose that the set of conjugacy class sizes of G is f1;m;mng, where m; n > 1 are coprime. We prove that m 1⁄4 p for some prime p dividing n 1. We also show that G has an abelian normal p-complement and that if P is a Sylow p-subgroup of G, then jP 0j 1⁄4 p and jP=ZðGÞpj 1⁄4 p. We obtain other properties and determine completely the structure of G.
متن کاملOn the Conjugacy Separability in the Class of Finite P -groups of Finitely Generated Nilpotent Groups
It is proved that for any prime p a finitely generated nilpotent group is conjugacy separable in the class of finite p-groups if and only if the tor-sion subgroup of it is a finite p-group and the quotient group by the torsion subgroup is abelian. 1. Let K be a class of groups. A group G is called residual K (or K-residual) if for each non-unit element a ∈ G there is a homomorphism ϕ of G onto ...
متن کاملFinite Index Subgroups of Conjugacy Separable Groups
We construct an example of conjugacy separable group possessing a not conjugacy separable subgroup of finite index. We give also a sufficient condition for a conjugacy separable group to preserve this property when passing to subgroups of finite index. We establish also conjugacy separability of finitely presented residually free groups using impressive results of Bridson and Wilton [BW-07].
متن کاملp-divisibility of conjugacy class sizes and normal p-complements
LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.05.022