Isomorph-dominating subgroup

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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
VIEW: Definitions built on this | Facts about this: (facts closely related to Isomorph-dominating subgroup, all facts related to Isomorph-dominating subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
Learn more about terminology local to the wiki | view a complete list of such terminology

Definition

A subgroup $H$ of a group $G$ is termed an isomorph-dominating subgroup if, for any subgroup $K$ of $G$ such that $H$ and $K$ are isomorphic groups, $K$ is contained in a conjugate subgroup of $H$, i.e., there exists $g\in G$ such that $K\le gH{g}^{-1}$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
homomorph-dominating subgroup	every homomorphic image is contained in a conjugate			|FULL LIST, MORE INFO
isomorph-containing subgroup	contains every isomorphic subgroup			|FULL LIST, MORE INFO
homomorph-containing subgroup	contains every homomorphic image			|FULL LIST, MORE INFO
isomorph-free subgroup	no other isomorphic subgroup			|FULL LIST, MORE INFO
isomorph-conjugate subgroup	conjugate to every isomorphic subgroup			|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
automorph-dominating subgroup	every automorph is contained in a conjugate			Template:Intermediate notionsshort	}