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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A theorem on nilpotent groups with restricted embeddings
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by Karl H. Wehrhahn PDF
Proc. Amer. Math. Soc. 54 (1976), 55-56 Request permission

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
    W. Burnside, On some properties of groups whose orders are powers of primes, Proc. London Math. Soc. (2) 11(1912), 225-245.
  • Charles Hobby, The Frattini subgroup of a $p$-group, Pacific J. Math. 10 (1960), 209–212. MR 113949
  • B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 54 (1976), 55-56
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0387405-9
  • MathSciNet review: 0387405