 # Rewriting Systems, Finiteness Conditions and Second Order Dehn Functions of Monoids

Wang, Jing (1998) Rewriting Systems, Finiteness Conditions and Second Order Dehn Functions of Monoids. PhD thesis, University of Glasgow.

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## Abstract

The main work of this thesis starts with Chapter 2. In Chapter 2, we first give some basic definitions and results about rewriting systems, then we consider finite complete rewriting systems for small extensions of monoids and for semi-direct products of monoids. After introducing the notion of directed 2-complex and some results about it, we consider subgroups of finite index in groups with finite complete rewriting systems. In Chapter 3, we first give some basic definitions and results about monoids of finite derivation type (FDT) and finite homological type (FHT), and their associated second order Dehn functions. Then we consider these properties for semi-direct products of monoids. We get that the class of FDT monoids and the class of FHT monoids are closed under semi-direct products. We also get some general bounds for second order Dehn functions of direct products of monoids. In Chapter 4, we continue to consider FDT, FHT and second order Dehn functions for some monoid constructions, such as small extensions and relative monoids. We get that the class of FDT monoids and the class of FHT monoids are closed under small extensions. Let S be a monoid, and let S0 be a submonoid of S such that S\S0 is an ideal of S. If S is FDT (respectively, FHT), then so is S0, and we have gammaS0(2) ≤ gammaS(2) respectively, gammaS0(2) ≤ gammaS(2)). For relative monoid S = S(R) with a coefficient group H, if LG(R) or RG(R) is cycle-free, then S is FDT (respectively, FHT) if and only if H is. We also get some relations between the second order Dehn functions of S and H.

Item Type: Thesis (PhD) Doctoral Adviser: S J Pride Mathematics 1998 Enlighten Team glathesis:1998-76447 Copyright of this thesis is held by the author. 19 Nov 2019 14:20 19 Nov 2019 14:20 http://theses.gla.ac.uk/id/eprint/76447 View Item