Locally subnormal subgroup

From Groupprops
Jump to: navigation, search
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
Subnormal subgroup |FULL LIST, MORE INFO

References

Textbook references

  • Subnormal subgroups of groups by John C. Lennox and Stewart E. Stonehewer, Oxford Mathematical Monographs, ISBN 019853552X, Page 216, More info