Automatic structures for subsemigroups of Baumslag–Solitar semigroups

Alan J. Cain
2013 Semigroup Forum  
This paper studies automatic structures for subsemigroups of Baumslag--Solitar semigroups (that is, semigroups presented by < x,y | (yx^m, x^ny) >, where m and n are natural numbers). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m n, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If m n, all of its finitely generated subsemigroups are left-automatic. If m = n, there exist finitely generated subsemigroups that
more » ... are not automatic. An appendix discusses the implications of these results for the theory of Malcev presentations. (A Malcev presentation is a special type of presentation for semigroups embeddable into groups.)
doi:10.1007/s00233-013-9490-y fatcat:5vlltwucjfayhjvfolwu33sugm