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On elementary groups


Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 26 (1970), 236-238
MSC: Primary 20.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0265467-1
Erratum: Proc. Amer. Math. Soc. 34 (1972), 631.
MathSciNet review: 0265467
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Abstract: Bechtell has defined a group $ G$ to be elementary if the Frattini subgroup of each subgroup of $ G$ is the identity. In this note we prove the following: If the derived group of $ G$ is nilpotent, then necessary and sufficient conditions that $ G$ be elementary are that the Frattini subgroup of $ G$ be the identity and that the Frattini subgroup of some Carter subgroup $ K$ of $ G$ be equal to the derived group of $ K$.


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

  • [1] H. Bechtell, Elementary groups, Trans. Amer. Math. Soc. 114 (1965), 355-362. MR 31 #243. MR 0175967 (31:243)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0265467-1
Keywords: Elementary group, Carter subgroup, Frattini subgroup
Article copyright: © Copyright 1970 American Mathematical Society

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