Complete rewriting system for the Schützenberger product of n groups

In this paper, we obtain a complete rewriting system for monoid presentation of Schützenberger product of [Formula: see text] groups, which is firstly defined in [G. M. S. Gomes, H. Sezinando and J. E. Pin, Presentations of the Schützenberger product of [Formula: see text] groups, Comm. Algebra 34(4) (2006) 1213–1235]. It gives an algorithm for getting normal form of elements and hence solving the word problem in this group.

PRESENTATION FOR RENNER MONOIDS

We extend the result obtained in E. Godelle [‘The braid rook monoid’, Internat. J. Algebra Comput.18 (2008), 779–802] to every Renner monoid: we provide a monoid presentation for Renner monoids, and we introduce a length function which extends the Coxeter length function and which behaves nicely.

A PRESENTATION OF THE DUAL SYMMETRIC INVERSE MONOID

The dual symmetric inverse monoid [Formula: see text] is the inverse monoid of all isomorphisms between quotients of an n-set. We give a monoid presentation of [Formula: see text] and, along the way, establish criteria for a monoid to be inverse when it is generated by completely regular elements.

A presentation for the monoid of uniform block permutations

The monoid n of uniform block permutations is the factorisable inverse monoid which arises from the natural action of the symmetric group on the join semilattice of equivalences on an n-set; it has been described in the literature as the factorisable part of the dual symmetric inverse monoid. The present paper gives and proves correct a monoid presentation forn. The methods involved make use of a general criterion for a monoid generated by a group and an idempotent to be inverse, the structure of factorisable inverse monoids, and presentations of the symmetric group and the join semilattice of equivalences on an n-set.

Monoid Presentations and Associated Groupoids

We consider properties of a 2-complex associated by Squier to a monoid presentation. We show that the fundamental groupoid admits a monoid structure, and we establish a relationship between its group completion and the fundamental group of the 2-complex. We also treat a modified complex, due to Pride, for monoid presentations of groups, and compute the structure of the fundamental groupoid in this setting.

On the Word Problem for Single Relation Monoids with an Unbordered Relator

Let A be an alphabet and u, v two words in A*. We show that the word problem is decidable for the monoid presentation [Formula: see text] if u is unbordered (i.e. non-self-overlapping), u is not a factor of v and |v| ≥ |u|2.