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Proceedings of the American Mathematical Society

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



A nonembedding theorem for finite groups

Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 25 (1970), 124-126
MSC: Primary 20.25
Erratum: Proc. Amer. Math. Soc. 34 (1972), 631.
MathSciNet review: 0258936
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Abstract: Let $ N$ be the class of nilpotent groups with the following properties: (1) The center of $ N,{Z_ \bot }(N)$ is of prime order. (2) There exists an abelian characteristic subgroup $ A$ of $ N$ such that $ {Z_1}(N) \subset A \subseteq {Z_2}(N)$ where $ {Z_2}(N)$ is the second term in the upper central series of $ N$. The main result shown is the following: $ N \in \mathfrak{X}$, then $ N$ cannot be an invariant subgroup contained in the Frattini subgroup of a finite group.

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

  • [1] C. Y. Chao, A theorem of nilpotent groups, Proc. Amer. Math. Soc. 19 (1968), 959-960. MR 37 #5295. MR 0229721 (37:5295)
  • [2] C. Hobby, The Frattini subgroup of a $ p$-group, Pacific J. Math. 10 (1960), 209-212. MR 22 #4780. MR 0113949 (22:4780)

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Keywords: Frattini subgroup
Article copyright: © Copyright 1970 American Mathematical Society

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