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Van Kampen Diagrams and Small Cancellation Theory

Given a presentation of G, the word problem asks whether there exists an algorithm to determine which words in the free group, F(A), represent the identity in G. In this thesis, we study small cancellation theory, developed by Lyndon, Schupp, and Greendlinger in the mid-1960s, which contributed to the resurgence of geometric group theory. We investigate the connection between Van Kampen diagrams and the small cancellation hypotheses. Groups that have a presentation satisfying the small cancellation hypotheses C'(1/6), or C'(1/4) and T(4) have a nice solution to the word problem known as Dehn’s Algorithm.

Identiferoai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-4045
Date01 June 2022
CreatorsLowrey, Kelsey N
PublisherDigitalCommons@CalPoly
Source SetsCalifornia Polytechnic State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMaster's Theses

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