Maximal subgroups of the minimal ideal of a free profinite monoid are free.
The author shows that the maximal subgroup of the minimal ideal of a finitely generated free profinite monoid is a free profinite group. This answers a question asked by S. W. Margolis in the 1990s. More generally, if \(\mathbf H\) is an extension-closed pseudovariety of finite groups that contains a cyclic \(p\)-group for infinitely many primes \(p\) and \(\overline{\mathbf H}\) is the pseudovariety of all finite monoids whose subgroups lie in \(\mathbf H\), then the maximal subgroup of the minimal ideal of a finitely generated free pro-\(\overline{\mathbf H}\) monoid is a free profinite group. Reviewer's remark. A further generalization has been obtained by \textit{A. Costa} and the author [Proc. Lond. Math. Soc. (3) 102, No. 2, 341-369 (2011; Zbl 1257.20054)].
scientific article; zbMATH DE number 5728344
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