Finite groups whose real classes have prime-power size

TL;DR

This paper characterizes finite groups where every real conjugacy class size is a prime power, providing insights into their structure and properties.

Contribution

It offers a new characterization of finite groups with all real class sizes as prime powers, advancing understanding of their algebraic structure.

Findings

All real classes have prime power size in the characterized groups

Structural properties of these groups are elucidated

The classification aids in understanding group symmetry and conjugacy class distribution

Abstract

We present a characterization of the finite groups in which all real classes have prime powers size.