Locally subnormal subgroup

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
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 |

Definition

A subgroup $H$ of a group $G$, is termed locally subnormal if, for every finitely generated subgroup $K$ of $G$, $H$ is a subnormal subgroup of $\langle H, K \rangle$.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
Permutable subgroup permutable implies locally subnormal |FULL LIST, MORE INFO
Normal subgroup (via subnormal) Subnormal subgroup|FULL LIST, MORE INFO