Nilpotency of normal subgroups having two 𝐺-class sizes-Reference-Cited by-同舟云学术

Nilpotency of normal subgroups having two 𝐺-class sizes

Published:2010-12-22 Issue:8 Volume:139 Page:2663-2669
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Alemany Elena,Beltrán Antonio,Felipe María

Abstract

Let G G be a finite group. If N N is a normal subgroup which has exactly two G G -conjugacy class sizes, then N N is nilpotent. In particular, we show that N N is abelian or is the product of a p p -group P P by a central subgroup of G G . Furthermore, when P P is not abelian, P / ( Z ( G ) ∩ P ) P/(\textbf {Z}(G)\cap P) has exponent p p .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2011-139-08/S0002-9939-2010-10702-5/S0002-9939-2010-10702-5.pdf

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