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Proceedings of the American Mathematical Society

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

 

 

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.


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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