An inequality detecting nilpotency of finite groups

2012/07/04 by Tom De Medts, Marius Tărnăuceanu, De Medts, Tom +1
Engineering · #20D15 #FOS: Mathematics #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1207.1020

openalex publication_date 2012/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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