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Groupprops β

Locally 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