# R-normal subgroup

From Groupprops

*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 of a finite group is termed **R-normal** if for any such that the orders of and are relatively prime, .

## Relation with other properties

### Stronger properties

## Metaproperties

### Intersection-closedness

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