Square-free class sizes in products of groups

We obtain some structural properties of a factorised group \(G = AB\), given that the conjugacy class sizes of certain elements in \(A\cup B\) are not divisible by \(p^2\), for some prime \(p\). The case when \(G = AB\) is a mutually permutable product is especially considered.

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-03
Main Authors: Felipe, M J, Martínez-Pastor, A, Ortiz-Sotomayor, V M
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We obtain some structural properties of a factorised group \(G = AB\), given that the conjugacy class sizes of certain elements in \(A\cup B\) are not divisible by \(p^2\), for some prime \(p\). The case when \(G = AB\) is a mutually permutable product is especially considered.
ISSN:2331-8422
DOI:10.48550/arxiv.1703.08363