Automorphically endomorph-dominating subgroup

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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]


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

Definition

A subgroup H of a group G is termed automorphically endomorph-dominating if, for any endomorphism \sigma of G, there exists an automorphism \varphi of G such that \sigma(H) \le \varphi(H).

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
endomorph-dominating subgroup image under any endomorphism is contained in one of its conjugate subgroups follows from the fact that conjugate subgroups are automorphic subgroups |FULL LIST, MORE INFO

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
subgroup whose characteristic closure is fully invariant its characteristic closure is a fully invariant subgroup |FULL LIST, MORE INFO
subgroup whose characteristic core is fully invariant its characteristic core is a fully invariant subgroup |FULL LIST, MORE INFO