Intersection of finitely many intermediately characteristic subgroups

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]

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Definition

A subgroup $H$ of a group $G$ is termed an intersection of finitely many intermediately characteristic subgroups in $G$ if there exists a collection $H_{1},H_{2},\dots ,H_{n}$ of $G$ such that $H=\bigcap _{i=1}^{n}H_{i}$, and such that each $H_{i}$ is an intermediately characteristic subgroup of $G$.

Formalisms

In terms of the finite intersection operator

This property is obtained by applying the finite intersection operator to the property: intermediately characteristic subgroup
View other properties obtained by applying the finite intersection operator

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
intermediately characteristic subgroup	characteristic in every intermediate subgroup	(obvious)	intermediate characteristicity is not finite-intersection-closed	|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
characteristic subgroup	invariant under all automorphisms	follows from characteristicity is strongly intersection-closed		|FULL LIST, MORE INFO