# Normal sub-APS

From Groupprops

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This term is related to: APS theory

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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: normal subgroup

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## Definition

Let be an APS of groups and be a sub-APS of . We say that is **normal** in if the following equivalent conditions hold:

- For every , is a normal subgroup of
- There exists an APS of groups and an APS homomorphism from to such that the kernel of the map at each is