An inequality detecting nilpotency of finite groups
Group Theory
2012-12-04 v2
Abstract
In this short note, we provide an inequality that holds in any finite group, only involving the orders of the elements; we prove that equality holds if and only if the group is nilpotent.
Keywords
Cite
@article{arxiv.1207.1020,
title = {An inequality detecting nilpotency of finite groups},
author = {Tom De Medts and Marius Tărnăuceanu},
journal= {arXiv preprint arXiv:1207.1020},
year = {2012}
}
Comments
As pointed out by Marty Isaacs, there is a mistake in the proof of Theorem 2 (taken from the American Mathematical Monthly) on which we rely. Theorem 2 is still conjecturally true, but reduces our main theorem to a conjecture. We have therefore withdrawn our paper