Free subgroups of free profinite groups

Random Normal Subgroups of Free Profinite Groups

Maximal abelian subgroups of free profinite groups

THEOREM. Let F be the free profinite group on a set X, where \X\ > 2, and let n be a non-empty set of primes. Then F has a maximal abelian subgroup isomorphic to HpEn Zp. The idea of the proof is the following: we show that A — Ylpe7I1p is a free factor of Pa, i.e. fia ^ A *B for some profinite group B. To conclude from this that A is a maximal abelian subgroup of Fa (the general case then foll...

Prosolvable Subgroups of Free Products of Profinite Groups

Frobenius Subgroups of Free Profinite Products

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.

on the free profinite products of profinite groups with commuting subgroups

in this paper we introduce the construction of free profinite products of profinite groups withcommuting subgroups. we study a particular case: the proper free profinite products of profinite groups with commuting subgroups. we prove some conditions for a free profinite product of profinite groups with commuting subgroups to be proper. we derive some consequences. we also compute profinite comp...