On free profinite subgroups of free profinite monoids

Abstract

We answer a question of Margolis from 1997 by establishing that the maximal subgroup of the minimal ideal of a finitely generated free profinite monoid is a free profinite group. More generally if $\mathbf{H}$ is variety of finite groups closed under extension and containing $\mathbb{Z}/p\mathbb{Z}$ for infinitely may primes $p$, the corresponding result holds for free pro-$\bar{\mathbf{H}}$ monoids.

References in corpus (1)

• Closed subgroups of free profinite monoids are projective profinite groups