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- Title
Wielandt 定理与非幂零极大子群指数皆为素数的有限群.
- Authors
田云凤; 史江涛; 刘文静
- Abstract
In order to give a further study of the solvability of a finite group in which every non-nilpotent maximal subgroup has prime index, the methods of the proof by contradiction and the counterexample of the smallest order and a theorem of Wielandt on the characterization of the structure of a finite group G with a nilpotent Hall-subgroup which is not a Sylow subgroup are applied to obtain a more elementary proof of the solvability of a finite group in which every non-nilpotent maximal subgroup has prime index. The proof does not apply the Glauberman-Thompson p-nilpotent criterion and Rose′s two results on a classification of non-abelian simple groups with nilpotent maximal subgroup and a characterization of non-solvable group with nilpotent maximal subgroup and trivial center respectively, which improves the proof of the result in the relevant research references.
- Subjects
NONABELIAN groups; FINITE groups; NILPOTENT groups; MAXIMAL subgroups; SYLOW subgroups; CONTRADICTION; CLASSIFICATION
- Publication
Journal of Harbin University of Science & Technology, 2023, Vol 28, Issue 3, p140
- ISSN
1007-2683
- Publication type
Article
- DOI
10.15938/j.jhust.2023.03.017