On the Number of Not Powers in a Finite Group
Group Theory
2018-11-06 v1
Abstract
Let G be a finite group and let k be a positive integer. We examine the relationship between structural properties of G and the number of elements of G that are not kth powers in G. In particular, we examine a bound on |G| given by Lucido and Pournaki and classify all cases when it is strict. We also show that when k is an odd prime, then either G has a normal subgroup with specific properties, or |G| is bounded above by a tighter function dependent on the number of not k-th powers of G.
Cite
@article{arxiv.1811.01898,
title = {On the Number of Not Powers in a Finite Group},
author = {William Cocke},
journal= {arXiv preprint arXiv:1811.01898},
year = {2018}
}
Comments
9 pages