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
View other analogues of normal subgroup | View other analogues in APSs of subgroup properties (OR, View as a tabulated list)
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