Finitely generated 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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This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definition
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Definition

Symbol-free definition

A group is said to be finitely generated if it has a finite generating set.

Relation with other properties

Stronger properties

• Finite group
• Finitely presented group: For proof of the implication, refer finitely presented implies finitely generated and for proof of its strictness (i.e. the reverse implication being false) refer finitely generated not implies finitely presented.
• Finitely generated free group

Weaker properties

• Countable group