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

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]


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

Weaker properties