Sub-isomorph-free subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a sub-isomorph-free subgroup if there exists an ascending chain of subgroups:

$$H = H_0 \le H_1 \le H_2 \le \dots \le H_n = G$$

such that each $$H_i$$ is an defining ingredient::isomorph-free subgroup of $$H_{i+1}$$.

Stronger properties

 * Weaker than::Isomorph-free subgroup

Weaker properties

 * Stronger than::Sub-(isomorph-normal characteristic) subgroup
 * Stronger than::Left-transitively WNSCDIN-subgroup
 * Stronger than::Characteristic subgroup
 * Stronger than::Normal subgroup