Malcev presentations for subsemigroups of direct products of coherent groups

Alan J. Cain

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The direct product of a free group and a polycyclic group is known to be coherent. This paper shows that every finitely generated subsemigroup of the direct product of a virtually free group and an abelian group admits a finite Malcev presentation. (A Malcev presentation is a presentation of a special type for a semigroup that embeds into a group. A group is virtually free if it contains a free subgroup of finite index.) By considering the direct product of two free semigroups, it is also shown that polycyclic groups, unlike nilpotent groups, can contain finitely generated subsemigroups that do not admit finite Malcev presentations. (C) 2008 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)977-990
Number of pages14
JournalJournal of Pure and Applied Algebra
Issue number6
Publication statusPublished - Jun 2009


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