Word Processing in GroupsThis study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to |
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abelian group accepted strings algorithm alphabet assume asynchronous automatic automatic groups automatic structure axioms b₁ basepoint biautomatic boundary component bounded braid group canonical form Cayley graph combable group compact compute cone points conjugate constant construct corresponding CW complex define Definition denote disk edge element of G endpoints equivalent euclidean fibre Figure finite number finite set finite state automaton follows fundamental group geodesic geometrically finite given group G groupoid hausdorff distance homotopy horoballs horosphere induction integer inverse image isoperimetric inequality L₁ labelled left-greedy Lemma length Let G lipschitz loop manifold metric space multiplier nilpotent pair path metric path of arrows permutation positive braid prefix prove pseudoisometry quasigeodesic quotient regular expression regular language representing result right-greedy rules S₁ satisfied Seifert semigroup ShortLex ShortLex order subgroup subset substring Suppose t₁ three-manifold torus u₁ uniform distance unique vertex vertices w₁ w₂