# Asymptotically fixed-depth join-transitively subnormal subgroup

From Groupprops

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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]

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

View other properties finitarily equivalent to subnormal subgroup | View other variations of subnormal subgroup |

This is a variation of join-transitively subnormal subgroup|Find other variations of join-transitively subnormal subgroup |

## Definition

A subgroup of a group is termed an **asymptotically fixed-depth join-transitively subnormal subgroup** if there exists a natural number such that for any , and any -subnormal subgroup of , the join is also a -subnormal subgroup of .

## Relation with other properties

### Stronger properties

### Weaker properties

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