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On maximal subgroups of free idempotent generated semigroups

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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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Authors and Affiliations

  1. Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    R. Gray

  2. School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK

    N. Ruskuc

Authors
  1. R. Gray
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  2. N. Ruskuc
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Correspondence to R. Gray.

Additional information

Supported by an EPSRC Postdoctoral Fellowship, and partially supported by FCT and FEDER, project POCTI-ISFL-1-143 of Centro de Álgebra da Universidade de Lisboa, and by the project PTDC/MAT/69514/2006.

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Gray, R., Ruskuc, N. On maximal subgroups of free idempotent generated semigroups. Isr. J. Math. 189, 147–176 (2012). https://doi.org/10.1007/s11856-011-0154-x

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  • DOI: https://doi.org/10.1007/s11856-011-0154-x

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