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

From Groupprops

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

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Contents

## 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 such that every subnormal subgroup of the group is -subnormal: its subnormal depth is at most .

## Relation with other properties

### Stronger properties

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