Subgroups of free idempotent generated semigroups need not be free

Details Subgroups of free idempotent generated semigroups need not be free Subgroups of free idempotent generated semigroups need not be free

2008-08-13

arxiv.org/abs/0808.1827v1

Mathematics

Group Theory

Scientific paper

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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