Finite groups in which almost all class sizes are prime numbers

Carmine Monetta; Víctor Sotomayor

doi:10.1007/s00605-026-02175-5

March 16, 2026Monatshefte für MathematikOpen Access

Finite groups in which almost all class sizes are prime numbers

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Key Points

The aim is to analyze the properties of finite groups that have primarily prime-sized conjugacy classes with few exceptions.
Analyzed the structure of finite groups based on conjugacy class sizes.
Identified and classified groups with exactly two composite class sizes.
Studied arithmetical features in relation to group structures.
Most class sizes in the studied finite groups are prime numbers.
Only two class sizes were found to be composite, suggesting a unique structural condition.
The findings indicate specific properties that such groups must possess.

Implication

Investigates class sizes in finite groups, showing implications of composite count on structure.

Abstract

In this paper we study arithmetical and structural features of a finite group that possesses exactly two conjugacy class sizes that are composite numbers.

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Cite This Study

Monetta et al. (2026) studied this question.

synapsesocial.com/papers/69ba43984e9516ffd37a50c2 https://doi.org/10.1007/s00605-026-02175-5

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Finite groups in which almost all class sizes are prime numbers

Key Points

Implication

Abstract

Discussion

Cite This Study

Finite groups in which almost all class sizes are prime numbers

Key Points

Implication

Abstract

Discussion

Cite This Study

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