Maximal subgroups of the minimal ideal of a free profinite monoid are free.

DOI10.1007/s11856-010-0023-zzbMath1220.20045OpenAlexW2009350950MaRDI QIDQ980498

Benjamin Steinberg

Publication date: 29 June 2010

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-010-0023-z

zbMATH Keywords

free profinite groupsminimal idealspseudovarieties of finite monoidsextension-closed pseudovarietiesfree profinite monoids

Mathematics Subject Classification ID

Ideal theory for semigroups (20M12) Applications of logic to group theory (20A15) Varieties and pseudovarieties of semigroups (20M07) Free semigroups, generators and relations, word problems (20M05) Limits, profinite groups (20E18)

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Presentations of Schützenberger groups of minimal subshifts. ⋮ A geometric interpretation of the Schützenberger group of a minimal subshift ⋮ Profinite topologies

Cites Work

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• On maximal pseudo-varieties of finite monoids and semigroups
• On solvable extensions of algebraic number fields
• Embedding Theorems for Semigroups
• Closed subgroups of free profinite monoids are projective profinite groups
• PROFINITE IDENTITIES FOR FINITE SEMIGROUPS WHOSE SUBGROUPS BELONG TO A GIVEN PSEUDOVARIETY
• PROFINITE SEMIGROUPS, VARIETIES, EXPANSIONS AND THE STRUCTURE OF RELATIVELY FREE PROFINITE SEMIGROUPS
• SUBWORD COMPLEXITY OF PROFINITE WORDS AND SUBGROUPS OF FREE PROFINITE SEMIGROUPS
• The automata theory of semigroup embeddings

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