On the structure of a finite solvable $K$-group
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- by Marshall Kotzen
- Proc. Amer. Math. Soc. 27 (1971), 16-18
- DOI: https://doi.org/10.1090/S0002-9939-1971-0268268-4
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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
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- Wolfgang Gaschütz, Über die $\Phi$-Untergruppe endlicher Gruppen, Math. Z. 58 (1953), 160–170 (German). MR 57873, DOI 10.1007/BF01174137
- Michio Suzuki, Structure of a group and the structure of its lattice of subgroups, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 10, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956. MR 0083487, DOI 10.1007/978-3-642-52758-6
- Giovanni Zacher, Caratterizzazione dei gruppi risolubili d’ordine finito complementati, Rend. Sem. Mat. Univ. Padova 22 (1953), 113–122 (Italian). MR 57878
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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