Sub-weakly marginal subgroup

Definition

A subgroup $H$ of a group $G$ is termed a sub-weakly marginal subgroup if there exists an ascending chain:

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

such that each $H_{i}$ is a weakly marginal subgroup of $H_{i+1}$.

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Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
marginal subgroup
weakly marginal subgroup
submarginal subgroup

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite direct power-closed characteristic subgroup
characteristic subgroup
normal subgroup