Israel Journal of Mathematics

, Volume 189, Issue 1, pp 147–176 | Cite as

On maximal subgroups of free idempotent generated semigroups

Article

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.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Centro de Álgebra da Universidade de LisboaLisboaPortugal
  2. 2.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsScotland, UK

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