On semigroups defined by Coxeter-type presentations
Colin Matthew Campbell, E. F. Robertson, Nik Ruškuc, Richard M. Thomas · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1995
Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.