Rational subgroups of biautomatic groups. (English) Zbl 0744.20035

The object of this article is to initiate the study of the subgroup structure of automatic groups. The authors show two main results: Centralizers of finite subsets in biautomatic groups are themselves biautomatic. Every polycyclic subgroup of a biautomatic group is Abelian-by-finite. The work includes a brief section on open problems.


20F65 Geometric group theory
20E07 Subgroup theorems; subgroup growth
53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
20F05 Generators, relations, and presentations of groups
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