English

Subgroups of free idempotent generated semigroups need not be free

Group Theory 2008-08-14 v1

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.

Keywords

Cite

@article{arxiv.0808.1827,
  title  = {Subgroups of free idempotent generated semigroups need not be free},
  author = {Mark Brittenham and Stuart W. Margolis and John Meakin},
  journal= {arXiv preprint arXiv:0808.1827},
  year   = {2008}
}