Right-transitively homomorph-containing subgroup

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Definition

A subgroup $K$ of a group $G$ is termed a right-transitively homomorph-containing subgroup if, whenever $H$ is a homomorph-containing subgroup of $K$, $H$ is also a homomorph-containing subgroup of $G$.

Relation with other properties

Stronger properties

• Subhomomorph-containing subgroup: For proof of the implication, refer subhomomorph-containing implies right-transitively homomorph-containing and for proof of its strictness (i.e. the reverse implication being false) refer right-transitively homomorph-containing not implies subhomomorph-containing.

Weaker properties

• Homomorph-containing subgroup