Conjugate-permuting subgroups

Symbol-free definition
Two subgroups of a group are said to be conjugate-permuting if the following equivalent conditions are satisfied:


 * Every conjugate of either permutes with every conjugate of the other.
 * Every conjugate of one permutes with the other subgroup
 * The first subgroup permutes with every conjugate of the other subgroup

Definition with symbols
Two subgroups $$H$$ and $$K$$ of a group $$G$$ are said to be conjugate-permuting if the following equivalent conditions are satisfied:


 * $$H^g$$ permutes with $$K^h$$ for every $$g,h \in G$$
 * $$H^g$$ permutes with $$K$$ for every $$g \in G$$
 * $$H$$ permutes with $$K^g$$ for every $$g \in G$$

Stronger relations

 * One is a seminormal subgroup and the other is a S-supplement of it

Weaker relations

 * Permuting subgroups