Intersections of Three Nilpotent Subgroups of Finite Groups


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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.

About the authors

V. I. Zenkov

Krasovskii Institute of Mathematics and Mechanics

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Email: v1i9z52@mail.ru
Russian Federation, Ekaterinburg

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