Intersections of Three Nilpotent Subgroups of Finite Groups
- 作者: Zenkov V.1
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隶属关系:
- Krasovskii Institute of Mathematics and Mechanics
- 期: 卷 60, 编号 4 (2019)
- 页面: 605-612
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172496
- DOI: https://doi.org/10.1134/S0037446619040062
- ID: 172496
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详细
Under study is the conjecture that for every three nilpotent subgroups A, B, and C of a finite group G there are elements x and y such that A ∩ Bx ∩ Cy ≤ F(G), where F(G) is the Fitting subgroup of G. We prove that a counterexample of minimal order to this conjecture is an almost simple group. The proof uses the classification of finite simple groups.
作者简介
V. Zenkov
Krasovskii Institute of Mathematics and Mechanics
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Email: v1i9z52@mail.ru
俄罗斯联邦, Ekaterinburg