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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A nonembedding theorem for finite groups
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by Ernest L. Stitzinger PDF
Proc. Amer. Math. Soc. 25 (1970), 124-126 Request permission

Erratum: Proc. Amer. Math. Soc. 34 (1972), 631.

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.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 124-126
  • MSC: Primary 20.25
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0258936-1
  • MathSciNet review: 0258936