# Group in which all subnormal subgroups have a common bound on subnormal depth

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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## Definition

A group in which all subnormal subgroups have a common bound on subnormal depth is a group for which there exists a natural number $k$ such that every subnormal subgroup of the group is $k$-subnormal: its subnormal depth is at most $k$.

## Relation with other properties

### Stronger properties

• Finite group
• Nilpotent group
• T-group: A T-group is a group where we can set $k = 1$.
• Group of finite composition length: If the composition length is $l$, the subnormal depth of any subgroup is bounded by $l - 1$. For full proof, refer: Composition length bounds subnormal depth of subnormal subgroups