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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A theorem on nilpotent groups with restricted embeddings


Author: Karl H. Wehrhahn
Journal: Proc. Amer. Math. Soc. 54 (1976), 55-56
MathSciNet review: 0387405
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Abstract | References | Additional Information

Abstract: Suppose that $ G$ is a nonabelian group with a unique proper normal subgroup of some given order. It is proved that $ G$ is not contained as a normal subgroup within the Frattini subgroup of a finite $ p$-group.


References [Enhancements On Off] (What's this?)

  • [1] W. Burnside, On some properties of groups whose orders are powers of primes, Proc. London Math. Soc. (2) 11(1912), 225-245.
  • [2] Charles Hobby, The Frattini subgroup of a 𝑝-group, Pacific J. Math. 10 (1960), 209–212. MR 0113949 (22 #4780)
  • [3] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703 (37 #302)


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0387405-9
PII: S 0002-9939(1976)0387405-9
Article copyright: © Copyright 1976 American Mathematical Society