2-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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Definition

A group is said to be 2-generated or is called a 2-generator group if it has a generating set comprising at most two elements.

Relation with other properties

Stronger properties

• Cyclic group
• Finite simple group

Weaker properties

• Finitely generated group