Subgroup contained in finitely many intermediate subgroups

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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]

Definition

Symbol-free definition

A subgroup of a group is said to be contained in finitely many intermediate subgroups if the number of subgroups of the whole group containing that subgroup is finite.

Definition with symbols

A subgroup H of a group G is said to be contained in finitely many intermediate subgroups if the number of subgroups K of G such that H \le K \le G is finite.

Relation with other properties

Stronger properties

Facts