Recursively presented group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group is said to be recursively presented if it possesses a recursive presentation, viz a presentation where:

• The number of generators is finite
• The set of relations is recursively enumerable

Relation with other properties

Stronger properties

• Finite group
• Finitely presented group

Weaker properties

• Finitely generated group
• Countable group