Purely definably generated subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup of a group is termed purely definably generated if it has a generating set that is a definable subset in terms of the first-order theory of the group.

Relation with other properties

Stronger properties

• Purely definable subgroup

Weaker properties

• Characteristic subgroup