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arXiv · 2103.17216

Finite groups can be generated by a pi-subgroup and a pi'-subgroup

Thomas Breuer·Robert M. Guralnick
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Abstract

Answering a question of Dan Haran and generalizing some results of Aschbacher-Guralnick and Suzuki, we prove that given a set of primes pi, any finite group can be generated by a pi-subgroup and a pi'-subgroup. This gives a free product description of a countably generated free profinite group.

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Thomas Breuer, Robert M. Guralnick. 2021-03-31. Finite groups can be generated by a pi-subgroup and a pi'-subgroup. https://arxiv.org/abs/2103.17216

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