Quasiautomorphism-invariant subgroup

Symbol-free definition
A subgroup of a group is termed quasiautomorphism-invariant if any quasiautomorphism of the whole group sends the subgroup to within itself.

A quasiautomorphism of a group is a quasihomomorphism of groups from the group to itself, with a two-sided inverse that is also a quasihomomorphism.

Formalisms
The following function restriction expression can be used for a quasiautomorphism-invariant subgroup:

Quasiautomorphism $$\to$$ Function

In other words, every quasiautomorphism of the whole group restricts to a function from the subgroup to itself.

An alternative expression is as the corresponding to quasiautomorphisms:

Quasiautomorphism $$\to$$ Quasiautomorphism

In other words, every quasiautomorphism of the whole group restricts to a quasiautomorphism from the subgroup to itself.

Stronger properties

 * Weaker than::Quasiendomorphism-invariant subgroup
 * Weaker than::1-automorphism-invariant subgroup
 * Weaker than::Quasihomomorph-containing subgroup

Weaker properties

 * Stronger than::Characteristic subgroup