Groups with some arithmetic conditions on real class sizes
Group Theory
2013-06-28 v1
Abstract
Let G be a finite group. An element x in G is a real element if x is conjugate to its inverse in G. For x in G, the conjugacy class x^G is said to be a real conjugacy class if every element of x^G is real. We show that if 4 divides no real conjugacy class size of a finite group G, then G is solvable. We also study the structure of such groups in detail. This generalizes several results in the literature.
Cite
@article{arxiv.1306.6369,
title = {Groups with some arithmetic conditions on real class sizes},
author = {Hung P. Tong-Viet},
journal= {arXiv preprint arXiv:1306.6369},
year = {2013}
}
Comments
9 pages