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