Normal subgroups contained in the Frattini subgroup
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- by W. Mack Hill and Charles R. B. Wright PDF
- Proc. Amer. Math. Soc. 35 (1972), 413-415 Request permission
Abstract:
Let H be a normal subgroup of the finite group G. If H has a subgroup K which is normal in G, satisfies $|K| > |K \cap {Z_1}(H)| = p$ and is not of nilpotence class 2, then H is not contained in the Frattini subgroup of G.References
- B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
- Ernest L. Stitzinger, A nonembedding theorem for finite groups, Proc. Amer. Math. Soc. 25 (1970), 124–126. MR 258936, DOI 10.1090/S0002-9939-1970-0258936-1
- Ernest L. Stitzinger, Errata for two papers of Stitzinger, Proc. Amer. Math. Soc. 34 (1972), 631. MR 294501, DOI 10.1090/S0002-9939-1972-0294501-X
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 413-415
- MSC: Primary 20D25
- DOI: https://doi.org/10.1090/S0002-9939-1972-0301094-7
- MathSciNet review: 0301094