Asymptotically fixed-depth join-transitively subnormal subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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If the ambient group is a finite group, this property is equivalent to the property: subnormal subgroup
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Definition

A subgroup $H$ of a group $G$ is termed an asymptotically fixed-depth join-transitively subnormal subgroup if there exists a natural number $n$ such that for any $k\geq n$, and any $k$-subnormal subgroup $K$ of $G$, the join $\langle H,K\rangle$ is also a $k$-subnormal subgroup of $G$.

Relation with other properties

Stronger properties

• Normal subgroup
• Subgroup of nilpotent group
• Subnormal subgroup of finite index: Also related:
  • Subnormal subgroup of finite group

Weaker properties

• Linear-bound join-transitively subnormal subgroup
• Polynomial-bound join-transitively subnormal subgroup
• Join-transitively subnormal subgroup
• Subnormal subgroup