On the orders of the non-Frattini elements of a finite group

2017/08/24 by Andrea Lucchini, Lucchini, Andrea
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1708.07331

arxiv created 2017/08/24 · arxiv updated 2017/08/25

Abstract

Let G be a finite group and let p₁,…,p_n be distinct primes. If G contains an element of order p₁⋯ p_n, then there is an element in G which is not contained in the Frattini subgroup of G and whose order is divisible by p₁⋯ p_n.

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