Elliptic subgroup

Symbol-free definition
A subgroup of a group is termed elliptic if it forms an elliptic pair of subgroups with every subgroup of the group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed elliptic if for any subgroup $$K$$ of $$G$$, $$(H,K)$$ form an elliptic pair of subgroups. In other words, there exists an $$n$$ such that:

$$\langle H,K \rangle = (HK)^n := HKHKHK \ldots HK$$

where each is written $$n$$ times.

Stronger properties

 * Permutable subgroup
 * Subgroup of finite index