R-normal subgroup

This article defines a subgroup property that makes sense within a finite group

This is a variation of normality|Find other variations of normality | Read a survey article on varying normality

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Definition

Symbol-free definition

A subgroup of a finite group is termed R-normal if it commutes with every element whose order is relatively prime to the order of the subgroup.

Definition with symbols

A subgroup $H$ of a finite group $G$ is termed R-normal if for any $x$ such that the orders of $x$ and $H$ are relatively prime, $Hx=xH$.

Relation with other properties

Stronger properties

• Normal subgroup

Metaproperties

Intersection-closedness

Is it true that an intersection of R-normal subgroups is R-normal?