Frobenius subgroups of free profinite products
Robert M. Guralnick (USC Los Angeles), Dan Haran (Tel Aviv University)
TL;DR
This paper proves that certain Frobenius groups appear as closed subgroups in free profinite products, resolving open problems related to prosolvable subgroups and their structure.
Contribution
It demonstrates the existence of specific Frobenius groups within free profinite products, addressing longstanding open questions in the field.
Findings
Frobenius groups occur as closed subgroups in free profinite products
Answers an open problem by Herfort and Ribes
Resolves a question posed by Pop about prosolvable subgroups
Abstract
We solve an open problem of Herfort and Ribes: Profinite Frobenius groups of certain type do occur as closed subgroups of free profinite products of two profinite groups. This also solves a question of Pop about prosolvable subgroups of free profinite products.
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