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arXiv · 0808.1827

Subgroups of free idempotent generated semigroups need not be free

Mark Brittenham·Stuart W. Margolis·John Meakin
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Abstract

We use topological methods to study the maximal subgroups of the free idempotent generated semigroup on a biordered set. We use these to give an example of a free idempotent generated semigroup with maximal subgroup isomorphic to the free abelian group of rank 2. This is the first example of a non-free subgroup of a free idempotent generated semigroup.

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Mark Brittenham, Stuart W. Margolis, John Meakin. 2008-08-13. Subgroups of free idempotent generated semigroups need not be free. https://arxiv.org/abs/0808.1827

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