Intersections of Three Nilpotent Subgroups of Finite Groups

Resumo

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 ∩ B^x ∩ C^y ≤ 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.