‘Malcev presentations for subsemigroups of groups — a survey’
In C. M. Campbell, M. Quick, E. F. Robertson, & G. C. Smith, eds, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, pp. 256–268 (Cambridge: Cambridge University Press, 2007).
DOI: 10.1017/CBO9780511721212.018. MR: 2328165.

Abstract

This paper introduces and surveys the theory of Malcev presentations. [Malcev presentations are a species of presentation that can be used to define any semigroup that can be embedded into a group.] In particular, various classes of groups and monoids all of whose finitely generated subsemigroups admit finite Malcev presentations are described; closure and containment results are stated; links with the theory of automatic semigroups are mentioned; and various questions asked. Many of the results stated herein are summarized in tabular form.