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Title:Artin Groups of Extra-Large Type Are Biautomatic
Author(s):Peifer, David Eugene
Doctoral Committee Chair(s):Schupp, Paul E.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:In this thesis we develop new techniques to work with small cancellation theory diagrams for Artin groups. Using these techniques we examine paths in the Cayley graph of the Artin group. For any Artin group G, with semigroup generators ${\cal A}$, we define a language $L(G) \subset {\cal A}\sp*$. The language L(G) is a set of canonical forms for the Artin group. In the case G is an Artin group of extra-large type or a two generator Artin group, we analyze the geometry of the small cancellation theory diagrams and show that L(G) is the language of a biautomatic structure for G.
Issue Date:1992
Type:Text
Description:103 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1992.
URI:http://hdl.handle.net/2142/72535
Other Identifier(s):(UMI)AAI9305653
Date Available in IDEALS:2014-12-17
Date Deposited:1992


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