Listar por tema "Conjugacy class sizes"
Mostrando ítems 1-9 de 9
-
A criterion for a normal subgroup to be hypercentral based on class sizes
Springer (2024)Let G be a finite group and N a normal subgroup of G. We prove that the knowledge of the sizes of the conjugacy classes of G that are contained in N and of their multiplicities provides information of N in relation to the ... -
Class sizes of prime-power orden p'-elements and normal subgroups
Springer (2014-06)We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p' -elements and prime- power order elements. Let N be a normal subgroup ... -
Corrigendum to "Variations on a theorem by Alan Camina on conjugacy class sizes" [J. Algebra 296 (2006) 253-266]
Elsevier (2008)[No abstract available]
-
Finite p-solvable groups with three p-regular conjugacy class sizes
Edinburgh Mathematical Society (2013)Let G be a finite p-solvable group. We describe the structure of the p-complements of G when the set of p-regular conjugacy classes has exactly three class sizes. For instance, when the set of p-regular class sizes of G ...
-
Normal subgroups and p-regular G-class sizes.
© 2011 Elsevier (2011-06)Let G be a finite p-solvable group and N be a normal subgroup of G. Suppose that the p-regular elements of N have exactly two G-conjugacy class sizes. In this paper it is shown that, if H is a p-complement of N, then either ...
-
On the Solvability of groups with four class sizes
World Scientific Publishing (2012)It is shown that if the set of conjugacy class sizes of a nite group G is f1; m; n;mng, where m; n are positive integers which do not divide each other, then G is up to central factors a fp; qg-group. In particular, G ...
-
Simplicity of normal subgroups and conjugacy class sizes
Springer (2013)Given a finite group G which possesses a non-abelian simple normal subgroup N having exactly four G -class sizes, we prove that N is isomorphic to PSL (2,2a) with a≥2 . Thus, we obtain an extension for normal subgroups of ...
-
Structure of normal subgroups with three G-class sizes
Springer-Verlag (2012)Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m < n and m does not divide n. In this paper, we show that N is solvable, and we determine ...
-
Structure of p -complements in groups with three p-regular class sizes
Springer-Verlag (2012)Let G be a finite p -solvable group for some prime p and suppose that the set of p -regular conjugacy class sizes is {1,m,mn} with (m,n)=1 and m coprime to p . We show that m=qb for some prime q and we describe the structure ...
