New bounds for numbers of primes in element orders of finite groups

2022/11/10 by Bellotti, Chiara, Keller, Thomas Michael, Trudgian, Timothy S.
#11N05 #20C15 #20D60 #20E34 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2211.05837

Abstract

Let ρ(n) denote the maximal number of different primes that may occur in the order of a finite solvable group G, all elements of which have orders divisible by at most n distinct primes. We show that ρ(n)≤ 5n for all n≥ 1. As an application, we improve on a recent bound by Hung and Yang for arbitrary finite groups.

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