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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$.

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)
  • [2] R. Carter, Nilpotent self-normalizing subgroups of soluble groups, Math. Z. 75 (1960/61), 136-139. MR 23 #A928. MR 0123603 (23:A928)
  • [3] W. Gaschütz, Über die $ \phi $-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160-170. MR 15, 285. MR 0057873 (15:285c)
  • [4] W. Scott, Group theory, Prentice-Hall, Englewood Cliffs, N. J., 1964. MR 29 #4785. MR 0167513 (29:4785)

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Keywords: Elementary group, Carter subgroup, Frattini subgroup
Article copyright: © Copyright 1970 American Mathematical Society

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