Biautomatic Structures on Groups via Group Actions

Date

2022

Authors

Trivedi, Vandit

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Abstract

Automatic groups are a special class of groups in which the word problem is decidable. It is not known whether every automatic group is biautomatic. The problem of obtaining an automatic or biautomatic structure assumes relevance in the interest of efficient computation in such groups. In this thesis, we introduce automatic and biautomatic groups, after which we consider methods to determine a biautomatic structure on a group through a group action on a geometric object. We conclude with an account of the result that $ \text{Aut}(B_{4}) $ is biautomatic.

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Keywords

automatic and biautomatic groups, group action, CAT(0) cube complex, systolic simplicial complex

Citation

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Type

Thesis (Masters)

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DOI

10.25911/RS27-7907

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