Strongly paranormal subgroup

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed strongly paranormal in $$G$$ if for any $$g \in G$$, the following identity holds:

$$[[g,H],H] = [g,H]$$

Here by $$[g,H]$$ we mean the subgroup generated by all commutators between $$g$$ and elements of $$H$$.

Stronger properties

 * Weaker than::Central subgroup

Weaker properties

 * Stronger than::Strongly polynormal subgroup
 * Stronger than::Paranormal subgroup
 * Stronger than::Polynormal subgroup
 * Stronger than::Weakly normal subgroup
 * Stronger than::Intermediately subnormal-to-normal subgroup
 * Stronger than::Subnormal-to-normal subgroup