Subgroups of free idempotent generated semigroups need not be free |
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| Authors: | Mark Brittenham Stuart W. Margolis John Meakin |
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| Affiliation: | 1. Department of Mathematics, University of Nebraska, Lincoln, NE 68588-0130, USA;2. Department of Mathematics, Bar Ilan University, 52900 Ramat Gan, Israel |
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| Abstract: | We study the maximal subgroups of free idempotent generated semigroups on a biordered set by topological methods. These subgroups are realized as the fundamental groups of a number of 2-complexes naturally associated to the biorder structure of the set of idempotents. We use this to construct the first example of a free idempotent generated semigroup containing a non-free subgroup. |
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