Sub-(isomorph-normal characteristic) subgroup

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Definition

A subgroup $H$ of a group $G$ is termed a sub-(isomorph-normal characteristic) subgroup if there exists an ascending chain of subgroups:

$H=H_{0}\leq H_{1}\leq H_{2}\leq \dots \leq H_{n}=G$

such that each $H_{i}$ is an isomorph-normal characteristic subgroup of $H_{i+1}$, i.e., $H_{i}$ is characteristic in $H_{i+1}$, and $H_{i}$ is isomorph-normal in $H_{i+1}$: every subgroup of $H_{i+1}$ isomorphic to $H_{i}$ is normal.

Relation with other properties

Stronger properties

• Isomorph-free subgroup
• Isomorph-normal characteristic subgroup
• Sub-isomorph-free subgroup

Weaker properties

• Characteristic subgroup

Metaproperties

Transitivity

This subgroup property is transitive: a subgroup with this property in a subgroup with this property, also has this property in the whole group.
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