Direct power-closed characteristic subgroup

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Definition

A subgroup $H$ of a group $G$ is termed a direct power-closed characteristic subgroup if for every cardinal $\alpha$, the subgroup $H^{\alpha }$ inside the direct power $G^{\alpha }$ (using the external direct product) is a characteristic subgroup of $G^{\alpha }$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
marginal subgroup		follows from marginality is direct power-closed and marginal implies characteristic		|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
finite direct power-closed characteristic subgroup				|FULL LIST, MORE INFO
characteristic subgroup				|FULL LIST, MORE INFO