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Proceedings of the American Mathematical Society

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

 

 

On elementary groups


Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 26 (1970), 236-238
MSC: Primary 20.40
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$.


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