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

2021/03/31 by Breuer, Thomas, Guralnick, Robert M.
#20D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2103.17216

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.

Related

• About isolators of finitely generated subgroups of free groups
• Virtually free pro-p products
• The probability of generating finite and profinite groups
• On the number of generators needed for free profinite products of finite groups
• Powers in finite groups