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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
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.

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

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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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