On the number of p-elements in a finite group

2020/07/02 by Gheri, Pietro · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2007.00967

Abstract

In this paper we study the ratio between the number of p-elements and the order of a Sylow p-subgroup of a finite group G. As well known, this ratio is a positive integer and we conjecture that, for every group G, it is at least the (1-(1)/(p))-th power of the number of Sylow p-subgroups of G. We prove this conjecture if G is p-solvable. Moreover, we prove that the conjecture is true in its generality if a somewhat similar condition holds for every almost simple group.

Cited by

• Covering the set of p-elements in finite groups by Sylow p-subgroups

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