Automorph-permutable 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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This is a variation of permutability|Find other variations of permutability |

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Definition

Symbol-free definition

A subgroup of a group is termed automorph-permutable if it permutes with any subgroup obtained as the image of it under an automorphism of the whole group.

Definition with symbols

A subgroup $H$ of a group $G$ is termed automorph-permutable if for any automorphism $\sigma$ of $G$, $H\sigma(H) = \sigma(H)H$.

Relation with other properties

Stronger properties

• Permutable subgroup
• Normal subgroup

Weaker properties

• Conjugate-permutable subgroup