# Left-transitively 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 **left-transitively homomorph-containing** if, for any group containing as a homomorph-containing subgroup, is also a homomorph-containing subgroup of .

## Relation with other properties

### Stronger properties

- Fully invariant direct factor:
`For full proof, refer: fully invariant direct factor implies left-transitively homomorph-containing`