一个检测有限群幂零性的不等式
群论
2012-12-04 v2
摘要
在这篇短文中，我们给出了一个在任何有限群中都成立的不等式，该不等式仅涉及元素的阶；我们证明了当且仅当该群为幂零群时等号成立。
引用
@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}
}
备注
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 We have therefore withdrawn our paper