On maximal subgroups of free idempotent generated semigroups

R. Gray, N. Ruskuc

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25 Citations (Scopus)

Abstract

We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister-Schreier type rewriting.
Original languageEnglish
Pages (from-to)147-176
Number of pages30
JournalIsrael Journal of Mathematics
Volume189
Issue number1
DOIs
Publication statusPublished - 2012

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