On maximal subgroups of free idempotent generated semigroups
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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.
Gray , R & Ruskuc , N 2012 , ' On maximal subgroups of free idempotent generated semigroups ' , Israel Journal of Mathematics , vol. 189 , no. 1 , pp. 147-176 . https://doi.org/10.1007/s11856-011-0154-x
Israel Journal of Mathematics
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