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Siberian Mathematical Journal

, Volume 60, Issue 4, pp 605–612 | Cite as

Intersections of Three Nilpotent Subgroups of Finite Groups

  • V. I. ZenkovEmail author
Article
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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 ABxCyF(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.

Keywords

finite group nilpotent subgroup intersection of subgroups Fitting subgroup 

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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsUral Federal UniversityEkaterinburgRussia

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