A generalization of Adjan’s theorem on embeddings of semigroups. (English) Zbl 1284.20065
Graphical diagrams which model transformations of words modulo defining relations are used to improve previously investigated sufficient conditions for a semigroup to be embeddable in a group [S. I. Adyan, Proc. Steklov Inst. Math. 85 (1966); translation from Tr. Mat. Inst. Steklov 85 (1966; Zbl 0204.01702); J. H. Remmers, Adv. Math. 36, 283-296 (1980; Zbl 0438.20041)] considering also defining relations of the form \(l=1\), i.e. monoids.
Reviewer: Jaak Henno (Tallinn)
MSC:
| 20M05 | Free semigroups, generators and relations, word problems |
| 20M15 | Mappings of semigroups |
| 20F10 | Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) |
| 20F06 | Cancellation theory of groups; application of van Kampen diagrams |
References:
| [1] | Adjan S. I., Proc. Steklov Inst. Math. 85 pp 3– (1966) |
| [2] | Bokut’ L. A., Uspekhi Mat. Nauk 42 pp 87– (1987) |
| [3] | Doss R., Bull. Sci. Math. 72 pp 139– (1948) |
| [4] | DOI: 10.4153/CJM-1951-005-8 · Zbl 0042.01701 · doi:10.4153/CJM-1951-005-8 |
| [5] | DOI: 10.1007/978-3-642-61896-3 · doi:10.1007/978-3-642-61896-3 |
| [6] | Malcev A., Mat. Sbornik (N.S.) 6 pp 331– (1939) |
| [7] | Malcev A., Mat. Sbornik (N.S.) 8 pp 251– (1940) |
| [8] | DOI: 10.1016/0001-8708(80)90018-3 · Zbl 0438.20041 · doi:10.1016/0001-8708(80)90018-3 |
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