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.
| Original language | English |
|---|---|
| Pages (from-to) | 3026-3042 |
| Number of pages | 17 |
| Journal | Journal of Algebra |
| Volume | 321 |
| Issue number | 10 |
| DOIs | |
| State | Published - 15 May 2009 |
Bibliographical note
Funding Information:E-mail addresses: [email protected] (M. Brittenham), [email protected] (S.W. Margolis), [email protected] (J. Meakin). 1 The first author acknowledges support from NSF Grant DMS-0306506. 2 The second author acknowledges support from the Department of Mathematics, University of Nebraska-Lincoln.
Funding
E-mail addresses: [email protected] (M. Brittenham), [email protected] (S.W. Margolis), [email protected] (J. Meakin). 1 The first author acknowledges support from NSF Grant DMS-0306506. 2 The second author acknowledges support from the Department of Mathematics, University of Nebraska-Lincoln.
| Funders | Funder number |
|---|---|
| Department of Mathematics, University of Nebraska-Lincoln | |
| National Science Foundation | DMS-0306506 |
| Directorate for Mathematical and Physical Sciences | 0306506 |
Keywords
- 2-complex
- Biordered set
- Combinatorial design
- Free idempotent generated semigroup