English

Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups

Group Theory 2024-07-31 v1

Abstract

Fixed point ratios for primitive permutation groups have been extensively studied. Relying on a recent work of Burness and Guralnick, we obtain further results in the area. For a prime pp and a finite group GG, we use fixed point ratios to study the number of Sylow pp-subgroups of GG and the minimal size of a covering by proper subgroups of the set of pp-elements of GG.

Keywords

Cite

@article{arxiv.2407.20355,
  title  = {Fixed point ratios, Sylow numbers and coverings of $p$-elements in finite groups},
  author = {Robert M. Guralnick and Attila Maróti and Juan Martínez Madrid and Alexander Moretó and Noelia Rizo},
  journal= {arXiv preprint arXiv:2407.20355},
  year   = {2024}
}