Recursively presented group

Definition
A group is said to be recursively presentable or recursively presented if it satisfies the following equivalent conditions:


 * 1) It possesses a defining ingredient::recursive presentation, i.e., a presentation where the set of generators is countably infinite (with an explicit enumeration) and the set of relations is recursively enumerable.
 * 2) It possesses a defining ingredient::recursive presentation, i.e., a presentation where the set of generators is countably infinite (with an explicit enumeration) and the set of relations is recursive.
 * 3) It is isomorphic to a subgroup of a defining ingredient::finitely presented group.