Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.797124
Title: Rewriting systems, finiteness conditions and second order Dehn functions of monoids
Author: Wang, Jing
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 1998
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.797124  DOI: Not available
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