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Groups, semigroups and finite presentations. (English) Zbl 0934.20036
Cossey, John (ed.) et al., Geometric group theory down under. Proceedings of a special year in geometric group theory, Canberra, Australia, July 14-19, 1996. Berlin: de Gruyter. 55-69 (1999).
This is a survey on the relationship between a semigroup and a group defined by the same presentation and the search for counterparts of classical group theoretic results in the semigroup setting. Although proofs are generally not given here the vehicle for much of the theory is that of so-called pictures which allow the study of presentations through a diagram of discs and arcs labelled by the given relations. Conditions under which the natural morphism from a semigroup to an identically presented group is injective or surjective are discussed along with results on presentation of subsemigroups, subsemigroups of finite index (defined in the paper), and free products.
For the entire collection see [Zbl 0910.00040].
MSC:
20M05 Free semigroups, generators and relations, word problems
20F05 Generators, relations, and presentations of groups
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