Action-isomorph-free 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

Definition with symbols

A subgroup H of a group G is termed action-isomorph-free in G if H is a normal subgroup of G, and the following condition holds.

Suppose \alpha:G \to \operatorname{Aut}(H) be the homomorphism induced by the action of G on H by conjugation. Suppose K is a normal subgroup of G with \beta:G \to \operatorname{Aut}(K) the homomorphism induced by the action of G on K by conjugation. Suppose, further, that \sigma:H \to K is an isomorphism with the property that:

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