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
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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