Polynomial-bound 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

Definition with symbols

A subgroup H of a group G is termed polynomial-bound join-transitively subnormal in G if there exists a polynomial f with integer coefficients such that if K is a k-subnormal subgroup of G, \langle H, K \rangle (the join of subgroups) is a f(k)-subnormal subgroup of G.

Here, a k-subnormal subgroup is a subgroup whose subnormal depth is at most k.

Relation with other properties

Stronger properties

Weaker properties