Listar por tema "conjugacy classes"
Mostrando ítems 1-8 de 8
-
An Arad and Fisman’s Theorem on Products of Conjugacy Classes Revisited
Springer (2022)A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A ∪ B or AB = A−1 ∪ B, then G cannot be a non-abelian simple group. We ... -
Conjugacy classes and union of cosets of normal subgroups
Springer Nature (2023)Let G be a finite group, N a normal subgroup of G and K a conjugacy class of G. We prove that if K∪K−1 is union of cosets of N, then N is soluble, K is a real-imaginary class, that is, every irreducible character of G takes ...
-
Conjugacy classes contained in normal subgroups: an overview
University of Isfahan (2017)We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an in uence on the normal structure of a nite group. The approach is mainly presented in the framework ...
-
Cosets of normal subgroups and powers of conjugacy classes
Wiley (2021-08-03)Let 𝐺 be a finite group and let𝐾 = 𝑥𝐺 be the conjugacy class of an element 𝑥 of 𝐺. In this paper, it is proved that if 𝑁 is a normal subgroup of 𝐺 such that the coset 𝑥𝑁 is the union of 𝐾 and 𝐾−1 (the conjugacy ...
-
Invariant class sizes and solvability of finite groups under coprime action
Wiley (2015)Suppose that A and G are finite groups of relatively prime orders such that A acts on G via automorphisms, and then, A acts on the set of conjugacy classes of G. We study several arithmetical properties on the sizes of ... -
Powers of conjugacy classes in a finite group
Springer (2019)The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning ...
-
Some problems about products of conjugacy classes in finite groups
University of Isfahan (2019-03)We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect ...
-
Squares of real conjugacy classes in finite groups
Springer Verlag (2017-07)We prove that if a finite group G contains a conjugacy class K whose square is of the form 1∪D, where D is a conjugacy class of G, then ⟨K⟩ is a solvable proper normal subgroup of G and we completely determine its structure. ...
