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:

$H=H_0\le H_1\le \dots \le H_n=G$

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

• Subgroup-cofactorial automorphism-invariant subgroup: Also related:
  • Left-transitively 2-subnormal subgroup
  • 2-subnormal subgroup
  • Subnormal subgroup