To the problem of extremal partition of the complex plane.

We consider one of the classical problems of the geometric theory of functions of a complex variable on a maximum of the functionalrB0.0rB∞∞γ∏k=1nrBkak,<graphic></graphic>where n ∈ ℕ, n ≥ 2, γ ∈ ℝ+, An=akk=1n<inline-graphic></inline-graphic> is a system of points such that |ak| = 1, a0 = 0, B0, B∞, Bkk=1n<inline-graphic></inline-graphic> is a system of pairwise nonoverlapping domains, ak∈Bk⊂ℂ¯<inline-graphic></inline-graphic>, k=0,n¯<inline-graphic></inline-graphic>, ∞∈B∞⊂ℂ¯<inline-graphic></inline-graphic>, r(B, a) is the inner radius of the domain B⊂ℂ¯<inline-graphic></inline-graphic> with respect to the point a ∈ B. We have analyzed this problem under some weaker restrictions on pairwise nonoverlapping domains. [ABSTRACT FROM AUTHOR]