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 Cofactorial automorphism-invariant subgroup|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 Subgroup-cofactorial automorphism-invariant subgroup|FULL LIST, MORE INFO
2-subnormal subgroup normal subgroup of a normal subgroup Left-transitively 2-subnormal subgroup, Subgroup-cofactorial automorphism-invariant subgroup|FULL LIST, MORE INFO
subnormal subgroup there is a subnormal series from it to the whole group Subgroup-cofactorial automorphism-invariant subgroup|FULL LIST, MORE INFO