Homomorph-containing subgroup
From Groupprops
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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 homomorph-containing if for any
, the image
is contained in
.
Relation with other properties
Weaker properties
- Fully characteristic subgroup
- Strictly characteristic subgroup
- Characteristic subgroup
- Isomorph-free subgroup in case the subgroup is co-Hopfian as a group: it is not isomorphic to any proper subgroup of itself.
Facts
- The omega subgroups of a group of prime power order are homomorph-containing. Further information: Omega subgroups are homomorph-containing