Biautomatic Structures on Groups via Group Actions
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.