Hereditarily 2-subnormal subgroup

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Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed a hereditarily 2-subnormal subgroup if, for any subgroup $K$ of $H$, $K$ is a 2-subnormal subgroup of $G$.

Formalisms

In terms of the hereditarily operator

This property is obtained by applying the hereditarily operator to the property: 2-subnormal subgroup
View other properties obtained by applying the hereditarily operator

Relation with other properties

Stronger properties

• Central subgroup
• Abelian normal subgroup
• Subgroup of abelian normal subgroup
• Dedekind normal subgroup
• Subgroup of Dedekind normal subgroup
• Subgroup contained in the Baer norm

Weaker properties

• Right-transitively 2-subnormal subgroup
• Hereditarily subnormal subgroup

Facts

• Centralizer of commutator subgroup is hereditarily 2-subnormal