Normal-homomorph-containing 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
A subgroup of a group
is termed normal-homomorph-containing if
is a normal subgroup of
, and for any homomorphism
such that
is also a normal subgroup of
, we have
.
Relation with other properties
Stronger properties
Weaker properties
- Weakly normal-homomorph-containing subgroup
- Strictly characteristic subgroup: For proof of the implication, refer Normal-homomorph-containing implies strictly characteristic and for proof of its strictness (i.e. the reverse implication being false) refer Strictly characteristic not implies normal-homomorph-containing. Also related:
- Normal-isomorph-containing subgroup