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Proceedings of the American Mathematical Society

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Frattini embeddings of normal subgroups


Author: C. R. B. Wright
Journal: Proc. Amer. Math. Soc. 78 (1980), 319-320
MSC: Primary 20D25
DOI: https://doi.org/10.1090/S0002-9939-1980-0553366-3
MathSciNet review: 553366
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Abstract | References | Similar Articles | Additional Information

Abstract: If N is a normal subgroup of the finite group G, there is a split extension X of an elementary abelian group by G such that $ N \trianglelefteq X$ and $ N \cap \Phi (G) = \Phi (X)$.


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

  • [1] R. B. J. T. Allenby, Normal subgroups contained in Frattini subgroups are Frattini subgroups, Proc. Amer. Math. Soc. 78 (1980), 315-318. MR 553365 (81g:20042)
  • [2] W. R. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 0167513 (29:4785)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0553366-3
Keywords: Frattini subgroup, embedding
Article copyright: © Copyright 1980 American Mathematical Society

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