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arXiv · 0712.2254

On free profinite subgroups of free profinite monoids

Benjamin Steinberg
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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.

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Benjamin Steinberg. 2007-12-13. On free profinite subgroups of free profinite monoids. https://arxiv.org/abs/0712.2254

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