A note on finite groups with few conjugacy classes of subgroups

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)≤5. A new characterization of A5 is also given.

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Publication Details

Journal
Communications in Algebra
Published
2026-07-25
DOI
https://doi.org/10.1080/00927872.2026.2703147
Primary Topic
Finite Group Theory Research
Type
article
Field-Weighted Citation Impact
0.00
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article

A note on finite groups with few conjugacy classes of subgroups

Marius Tărnăuceanu
Communications in Algebra
Finite Group Theory Research
article

A note on finite groups with few conjugacy classes of subgroups

Marius Tărnăuceanu
article en

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)≤5. A new characterization of A5 is also given.

Communications in Algebra
Alexandru Ioan Cuza University (RO)
Openalex Percentile: Top 3%
Finite Group Theory Research
DOISourceOpenAlex
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