On Conjugacy Class Sizes of the p′-Elements with Prime Power Order-Reference-Cited by-同舟云学术

On Conjugacy Class Sizes of the p′-Elements with Prime Power Order

Published:2009-12 Issue:04 Volume:16 Page:541-548
ISSN:1005-3867
Container-title:Algebra Colloquium
language:en
Short-container-title:Algebra Colloq.

Author:

Zhao Xianhe¹,Guo Xiuyun¹

Affiliation:

1. Department of Mathematics, Shanghai University, Shanghai 200444, China

Abstract

In this paper we prove that a finite p-solvable group G is solvable if its every conjugacy class size of p′-elements with prime power order equals either 1 or m for a fixed integer m. In particular, G is 2-nilpotent if 4 does not divide every conjugacy class size of 2′-elements with prime power order.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1005386709000510

Reference16 articles.

1. Group elements of prime power index

2. Finite groups with two p-regular conjugacy class lengths

3. On groups with abelian Sylow 2-subgroups

4. Indices of elements and normal structure of finite groups

5. On a Graph Related to Conjugacy Classes of Groups

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2. The Influence of Conjugacy Class Sizes on the Structure of Finite Groups;Taiwanese Journal of Mathematics;2017-08-01

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5. ITÔ’S THEOREM ON GROUPS WITH TWO CLASS SIZES REVISITED;Bulletin of the Australian Mathematical Society;2011-10-19