A note on finite groups with few conjugacy classes of subgroups

Marius Tărnăuceanu

A note on finite groups with few conjugacy classes of subgroups

Group Theory 2026-07-06 v1

Authors: Marius Tărnăuceanu

Abstract

In this note, we give some conditions of solvability of a finite group $G$ based on its number of conjugacy classes of subgroups $Con(G)$ . We classify all finite groups $G$ with $Con(G)\leq 5$ . A new characterization of $A_5$ is also given.

Keywords

finite groups conjugacy classes of subgroups solvability classification A5

Cite

@article{arxiv.2607.05700,
  title  = {A note on finite groups with few conjugacy classes of subgroups},
  author = {Marius Tărnăuceanu},
  journal= {arXiv preprint arXiv:2607.05700},
  year   = {2026}
}

Comments

Accepted for publication in Comm. Algebra