On finite groups containing three 𝐶𝐶-subgroups

Abstract

Abstract.A finite group G has a self-centralization system of type (2|y4,|, 4|/42|,4|j43|) if G contains three nonconjugate CC-subgroups Ax, A2, A3, such that \Na(Ax)\ = 2\AX\, |^VC(^2)I = 4l^2l. \N<A*ù\ -*\Ai\-The authors prove that if a finite group G has a self-centralization system of type (2\AX\, 4\A2\, 4|/43|) and |G| < 3|ii,|2|^2|2|i<3|2, then G has a nilpotent normal subgroup N such that G/N is isomorphic to Sz(q) for suitable q.