An automatic group is a finitely generated group satisfying the following equivalent conditions:
- There exists a finite generating set with respect to which the group possesses a biautomatic structure.
- For every finite generating set, the group possesses a biautomatic structure with respect to that generating set.
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions