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 is variety of finite groups closed under extension and containing ℤ/pℤ for infinitely may primes p, the corresponding result holds for free pro-\( \bar H \) monoids.
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The author was supported in part by NSERC.
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Steinberg, B. Maximal subgroups of the minimal ideal of a free profinite monoid are free. Isr. J. Math. 176, 139–155 (2010). https://doi.org/10.1007/s11856-010-0023-z
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DOI: https://doi.org/10.1007/s11856-010-0023-z