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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. II


Author: W. Mack Hill
Journal: Proc. Amer. Math. Soc. 53 (1975), 277-279
MSC: Primary 20D25
DOI: https://doi.org/10.1090/S0002-9939-1975-0390051-3
MathSciNet review: 0390051
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Abstract: If $ p$ is an odd prime and $ H$ is a $ p$-group with a characteristic subgroup $ K$ such that $ \vert K\vert > \vert K \cap Z(H)\vert = p$, then $ H$ cannot be a normal subgroup contained in the Frattini subgroup of any finite group $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0390051-3
Keywords: Extra-special $ p$-group, Frattini subgroup
Article copyright: © Copyright 1975 American Mathematical Society