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

Guralnick, Robert M. and Maróti, Attila and Martínez Madrid, Juan and Moretó, Alexander and Rizo, Noelia (2025) Fixed‐point ratios, Sylow numbers, and coverings of p‐elements in finite groups. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 111 (5). ISSN 0024-6107

Text 2407.20355v1.pdf - Published Version Restricted to Repository staff only Download (296kB) | Request a copy

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 p and a finite group G, we use fixed point ratios to study the number of Sylow p-subgroups of G and the minimal size of a covering by proper subgroups of the set of p-elements of G.

Actions (login required)

Edit Item