On finite groups whose Sylow subgroups have a bounded number of generators

2010/03/24 by Colin D. Reid, Reid, Colin D.
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1003.4722

openalex publication_date 2010/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finite non-nilpotent group such that every Sylow subgroup of G is generated by at most d elements, and such that p is the largest prime dividing |G|. We show that G has a non-nilpotent image G/N, such that N is characteristic and of index bounded by a function of d and p. This result will be used to prove that the index of the Frattini subgroup of G is bounded in terms of d and p. Upper bounds will be given explicitly for soluble groups.

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