Locally subnormal subgroup
From Groupprops
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 |
Contents
Definition
A subgroup of a group , is termed locally subnormal if, for every finitely generated subgroup of , is a subnormal subgroup of .
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}