NSCFN-subgroup
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
Symbol-free definition
A subgroup of a group is termed a NSCFN-subgroup if it is normal, fully normalized and self-centralizing in the whole group.
Definition with symbols
A subgroup of a group
is termed a NSCFN-subgroup if
,
is fully normalized in
, and
.
Equivalently, is a NSCFN-subgroup of
if
is a normal subgroup of
, and the induced homomorphism
induced by the conjugation action is surjective with kernel equal to
.