R-normal subgroup

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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


This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

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

Metaproperties

Intersection-closedness

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