Sub-cofactorial automorphism-invariant subgroup

Definition

A subgroup $H$ of a group $G$ is termed a sub-cofactorial automorphism-invariant subgroup if there exists an ascending chain of subgroups:

$H=H_{0}\leq H_{1}\leq \dots \leq H_{n}=G$

such that each $H_{i}$ is a cofactorial automorphism-invariant subgroup of $G$.

Formalisms

In terms of the subordination operator

This property is obtained by applying the subordination operator to the property: cofactorial automorphism-invariant subgroup
View other properties obtained by applying the subordination operator

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
characteristic subgroup	invariant under all automorphisms			|FULL LIST, MORE INFO
cofactorial automorphism-invariant subgroup	invariant under all cofactorial automorphisms		cofactorial automorphism-invariance is not transitive	|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Subgroup-cofactorial automorphism-invariant subgroup	invariant under all subgroup-cofactorial automorphisms			|FULL LIST, MORE INFO
left-transitively 2-subnormal subgroup	whenever the group is 2-subnormal in a bigger group, so is the subgroup			|FULL LIST, MORE INFO
2-subnormal subgroup	normal subgroup of a normal subgroup			|FULL LIST, MORE INFO
subnormal subgroup	there is a subnormal series from it to the whole group			|FULL LIST, MORE INFO