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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
DOI: https://doi.org/10.1090/S0002-9939-1970-0258936-1
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.


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