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Normal subgroups contained in the Frattini subgroup


Authors: W. Mack Hill and Charles R. B. Wright
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
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Abstract: Let H be a normal subgroup of the finite group G. If H has a subgroup K which is normal in G, satisfies $ \vert K\vert > \vert K \cap {Z_1}(H)\vert = p$ and is not of nilpotence class 2, then H is not contained in the Frattini subgroup of G.


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

  • [1] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
  • [2] E. L. Stitzinger, A nonembedding theorem for finite groups, Proc. Amer. Math. Soc. 25 (1970), 124-126. MR 41 #3581. MR 0258936 (41:3581)
  • [3] -, Errata, Proc. Amer. Math. Soc. 34 (1972), 631. MR 0294501 (45:3571)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0301094-7
Keywords: p-group, normal subgroup, Frattini subgroup
Article copyright: © Copyright 1972 American Mathematical Society

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