Finite groups can be generated by a -subgroup and a С-subgroup
ISRAEL JOURNAL OF MATHEMATICS(2023)
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 new free product description of a free profinite group.
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