The number of composite class sizes in finite groups

Vittorio Bagnara; Víctor Sotomayor

The number of composite class sizes in finite groups

Group Theory 2026-06-26 v1

Authors: Vittorio Bagnara , Víctor Sotomayor

Abstract

We consider finite groups with at least three conjugacy class sizes that are composite numbers and we prove that, in that situation, the number of prime class sizes is bounded by the number of composite class sizes. The analogous result for (non-)prime-power class sizes is also addressed.

Keywords

finite groups conjugacy class sizes composite numbers prime numbers prime-power

Cite

@article{arxiv.2606.27977,
  title  = {The number of composite class sizes in finite groups},
  author = {Vittorio Bagnara and Víctor Sotomayor},
  journal= {arXiv preprint arXiv:2606.27977},
  year   = {2026}
}