Strongly proper sub-APS

This article defines a group sub-IAPS property: a property that can be evaluated to true/false given an APS of groups and a sub-APS.

Definition

Let $(G,\mathrm{\Phi })$ be an APS of groups. A sub-APS $H$ of $G$ is termed strongly proper if $H_m$ is a proper subgroup of $G_m$ for infinitely many $m$.