Totally permuting subgroups

This article defines a symmetric relation on the collection of subgroups inside the same group.

This is a variation of permuting subgroups|Find other variations of permuting subgroups |

Definition

Symbol-free definition

Two subgroups of a group are said to be totally permuting if every subgroup of either permutes with every subgroup of the other.

Definition with symbols

Two subgroups $H$ and $K$ of a group $G$ are said to be totally permuting if for every subgroup $M$ of $H$ and every subgroup $N$ of $K$, $MN=NM$.

Relation with other relations

Weaker relations

• Mutually permuting subgroups
• Permuting subgroups