The word problem for finitely presented special inverse monoids

Warne, Jonathan Henry (2025) The word problem for finitely presented special inverse monoids. Doctoral thesis, University of East Anglia.

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Abstract

In this thesis we investigate the decidability of the word problem for finitely presented special inverse monoids via the prefix membership problem of their maximal group images. The work can be divided into two tranches which use distinct methods.

In the first tranche we approach the problem via a factorisation of the inverse monoid’s relators. We show that there are two combinatorial conditions on the factors which when present in conjunction with certain other conditions are sufficient to decide the word problem of the inverse monoid. Further we demonstrate that when these conditions apply to minimal invertible factorisations that there is an equivalence between the word problems of the inverse monoid, its group of units and its maximal group image.

In the second tranche we approach the problem via the Magnus Moldavanski˘i hierarchy. We show that a family of HNN extensions of the free group have qualities which are algorithmically useful. In particular we are able to demonstrate that this means such HNN extensions have a class of submonoids with decidable word problem. We can then apply these results to solve the prefix membership problem in several examples.

Additionally we are able to provide a number of sufficient conditions for the amalgamated product of two E-unitary inverse monoids to be itself E-unitary.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
Depositing User:	Chris White
Date Deposited:	11 Feb 2026 11:42
Last Modified:	11 Feb 2026 11:42
URI:	https://ueaeprints.uea.ac.uk/id/eprint/101912
DOI:

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