Isomorph-automorphic subgroup

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

Symbol-free definition

A subgroup of a group is termed isomorph-automorphic if given any other isomorphic subgroup, there is an automorphism of the whole group, mapping the subgroup isomorphically to the other one.

Definition with symbols

A subgroup $H$ of a group $G$ is termed isomorph-automorphic if whenever there exists a subgroup $K$ of $G$ such that $H$ and $K$ are isomorphic groups, there exists an automorphism $\sigma$ of $G$ such that $\sigma (H)=K$.

Relation with other properties

Stronger properties

• Sylow subgroup
• Order-unique subgroup
• Order-automorphic subgroup
• Order-conjugate subgroup
• Isomorph-conjugate subgroup
• Isomorph-free subgroup