Isolated subgroups of finite abelian groups

2021/02/09 by Marius Tărnăuceanu, Tărnăuceanu, Marius
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.2102.04598

arxiv created 2021/02/09 · openalex publication_date 2021/02/09 · arxiv updated 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We say that a subgroup H is isolated in a group G if for every x∈ G we have either x∈ H or ⟨ x⟩∩ H=1. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.

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