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Finite Groups with Normal Normalizers

Published online by Cambridge University Press:  20 November 2018

C. Hobby
C. Hobby*
Affiliation:
University of Washington, Seattle, Washington
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We say that a finite group G has property N if the normalizer of every subgroup of G is normal in G. Such groups are nilpotent since every Sylow subgroup is normal (the normalizer of a Sylow subgroup is its own normalizer). Thus it is sufficient to study p-groups which have property N. Note that property N is inherited by subgroups and factor groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1256 - 1260
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

This research was supported jointly by the National Science Foundation under grant GR-5691 and by the Air Force Office of Scientific Research under contract AF-AFOSR-937-65.

References

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5. Hobby, C., A characteristic subgroup of a p-group, Pacific J. Math. 10 (1960), 853–858.Google Scholar