Subisomorph-containing subgroup

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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]
If the ambient group is a finite group, this property is equivalent to the property: variety-containing subgroup
View other properties finitarily equivalent to variety-containing subgroup | View other variations of variety-containing subgroup |

Definition

A subgroup H of a group G is termed subisomorph-containing if whenever K is a subgroup of G and L is a subgroup of H such that K and L are isomorphic, then L is also a subgroup of H.

Relation with other properties

In groups with specific properties

Stronger properties

Weaker properties