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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

1. Burnside, W., On groups in which every two conjugate operations are permutable, Proc. London Math. Soc. 35 (1902), 28–37.Google Scholar
2. Hall, M., The theory of groups (Macmillan, New York, 1959).Google Scholar
3. Hall, P., A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. (2) 36 (1933), 29–95.Google Scholar
4. Hall, P., On a theorem of Frobenius, Proc. London Math. Soc. (2) 4-0 (1935), 468–501.Google Scholar
5. Hobby, C., A characteristic subgroup of a p-group, Pacific J. Math. 10 (1960), 853–858.Google Scholar