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arXiv · 1003.4722

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

Colin D. Reid
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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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Colin D. Reid. 2010-04-13. On finite groups whose Sylow subgroups have a bounded number of generators. https://arxiv.org/abs/1003.4722

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