English

On free profinite subgroups of free profinite monoids

Group Theory 2007-12-17 v1

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 H\mathbf H is variety of finite groups closed under extension and containing Z/pZ\mathbb Z/p\mathbb Z for infinitely may primes pp, the corresponding result holds for free pro-Hˉ\bar{\mathbf H} monoids.

Keywords

Cite

@article{arxiv.0712.2254,
  title  = {On free profinite subgroups of free profinite monoids},
  author = {Benjamin Steinberg},
  journal= {arXiv preprint arXiv:0712.2254},
  year   = {2007}
}