Email this article Intersections of Three Nilpotent Subgroups of Finite Groups
- Authors: Zenkov V.I.1
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Affiliations:
- Krasovskii Institute of Mathematics and Mechanics
- Issue: Vol 60, No 4 (2019)
- Pages: 605-612
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172496
- DOI: https://doi.org/10.1134/S0037446619040062
- ID: 172496
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Abstract
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.
About the authors
V. I. Zenkov
Krasovskii Institute of Mathematics and Mechanics
Author for correspondence.
Email: v1i9z52@mail.ru
Russian Federation, Ekaterinburg
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