Bass–Serre Theory for Groupoids and the Structure of Full Regular Semigroup Amalgams
✍ Scribed by Stephen Haataja; Stuart W. Margolis; John Meakin
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 202 KB
- Volume
- 183
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
U have the same set of idempotents , then the amalgam is strongly embeddable in a regular semigroup S that contains S , S , and U as full regular subsemigroups. In 1 2
this case the inductive structure of the amalgamated free produce S ) S was 1 U 2 studied by Nambooripad and Pastijn in 1989, using Ordman's results from 1971 on amalgams of groupoids. In the present paper we show how these results may be combined with techniques from Bass᎐Serre theory to elucidate the structure of the maximal subgroups of S ) S . This is accomplished by first studying the appropri-1 U 2 ate analogue of the Bass᎐Serre theory for groupoids and applying this to the study of the maximal subgroups of S ) S . The resulting graphs of groups are arbitrary 1 U 2 bipartite graphs of groups. This has several interesting consequences. For example if S and S are combinatorial, then the maximal subgroups of S ) S are free 1 2 1 U 2 groups. Finite inverse semigroups may be decomposed in non-trivial ways as amalgams of inverse semigroups.