# Biautomatic group

From Groupprops

## Definition

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 propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions