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This research aims to explore conditions for the solvability of finite groups based on their conjugacy classes of subgroups.

July 27, 2026Communications in Algebra

A note on finite groups with few conjugacy classes of subgroups

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This research aims to explore conditions for the solvability of finite groups based on their conjugacy classes of subgroups.
Classified finite groups with Con(G)≤5
Provided conditions for solvability
Characterized the group A5.
Identified all finite groups with 5 or fewer conjugacy classes of subgroups
Established new criteria for the solvability of certain finite groups
Presented a new characterization of the group A5.

Implication

Note examines solvability conditions in finite groups based on subgroup conjugacy classes, highlighting A5.

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.

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Cite This Study

Marius Tărnăuceanu (2026) studied this question.

synapsesocial.com/papers/6a6700a340bca442e0d4a811 https://doi.org/10.1080/00927872.2026.2703147

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Implication

Note examines solvability conditions in finite groups based on subgroup conjugacy classes, highlighting A5.

A note on finite groups with few conjugacy classes of subgroups

Key Points

Implication

Abstract

Discussion

Cite This Study

A note on finite groups with few conjugacy classes of subgroups

Key Points

Implication

Abstract

Discussion

Cite This Study

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