Strongly polynormal subgroup

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Definition

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

$[[<g>,H],H]=[<g>,H]$

Here $[K,L]$ denotes the subgroup generated by commutators between elements of $K$ and elements of $L$.

Relation with other properties

Stronger properties

• Strongly paranormal subgroup

Weaker properties

• Polynormal subgroup

References

• On the arrangement of subgroups normalized by a fixed subgroup by A. V. Stepanov, Zap. Nauchn. Semin. LOMI, 198, 92-102 (1991)