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]
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 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 \ge 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

Weaker properties

Metaproperties

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