Order-dominating 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]

Definition

Symbol-free definition

A finite subgroup of a group is termed order-dominating if every other subgroup whose order divides its order, is conjugate to a subgroup contained in it.

Definition with symbols

Let G be a group and H be a finite subgroup. Then, H is termed order-dominating in G if, for any subgroup K \le G such that the order of K divides the order of G, there exists g \in G such that gKg^{-1} \le H.

Relation with other properties

Stronger properties

Weaker properties