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Proceedings of the American Mathematical Society

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

 
 

 

On the structure of a finite solvable $ K$-group


Author: Marshall Kotzen
Journal: Proc. Amer. Math. Soc. 27 (1971), 16-18
MSC: Primary 20.27
DOI: https://doi.org/10.1090/S0002-9939-1971-0268268-4
MathSciNet review: 0268268
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Abstract: In this note we investigate the structure of a finite solvable $ K$-group. It is proved that a finite group $ G$ is a solvable $ K$-group if and only if $ G$ is a subdirect product of a finite collection of solvable $ K$-groups $ {H_i}$ such that each $ {H_i}$ is isomorphic to a subgroup of $ G$, and each $ {H_i}$ possesses a unique minimal normal subgroup.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0268268-4
Keywords: Solvable group, $ K$-group, subdirect product, unique minimal normal subgroup, series, maximal normal nilpotent subgroup, Frattini subgroup, Fitting group, elementary abelian, $ G$ splits over $ F(G)$, completely reducible, direct product
Article copyright: © Copyright 1971 American Mathematical Society

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