Conjugacy-closed sub-APS

This article gives a property that can be evaluated for a sub-APS in an APS of groups

ANALOGY: This is an analogue in APS of a property encountered in group. Specifically, it is a sub-APS property analogous to the subgroup property: conjugacy-closed subgroup
View other analogues of conjugacy-closed subgroup | View other analogues in APSs of subgroup properties (OR, View as a tabulated list)

Definition

A sub-APS $H$ of an APS of groups $(G,\Phi )$ is termed conjugacy-closed if for every $n$, $H_{n}$ is a conjugacy-closed subgroup of $G_{n}$: in other words, whenever two elements of $H_{n}$ are conjugate in $G_{n}$, they are also conjugate in $H_{n}$.