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Proceedings of the American Mathematical Society

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

 

 

Normal subgroups contained in Frattini subgroups are Frattini subgroups


Author: R. B. J. T. Allenby
Journal: Proc. Amer. Math. Soc. 78 (1980), 315-318
MSC: Primary 20D25
DOI: https://doi.org/10.1090/S0002-9939-1980-0553365-1
MathSciNet review: 553365
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Abstract: We prove that if N is a normal subgroup of the finite group G and if $ N \subseteq \Phi (G)$, then there exists a finite group U such that $ N = \Phi (U)$ exactly. In particular, we see that the generalizations apparent in the conclusions of several recently stated theorems are illusory.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0553365-1
Keywords: Frattini subgroup, (generalized) free product, free group, wreath product, alternating group
Article copyright: © Copyright 1980 American Mathematical Society