Subgroups of free idempotent generated semigroups need not be free
By Mark Brittenham, Stuart W. Margolis, J. Meakin. 2008
57 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aa72c896450d72722f851dd59ced7992a8cc99e7
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On maximal subgroups of free idempotent generated semigroups (2009, methodology): “The first counterexample to this conjecture was given by Brittenham, Margolis and Meakin [1], where it was shown that the free abelian group Z ⊕ Z is the maximal subgroup of the free idempotent generated semigroup arising from a certain 72-element semigroup.”