On some results by S. Belkov and I. Korepanov

This note is purely expositional and is a complement to math review MR2730150 to the paper Bel'kov, S. I.; Korepanov, I. G. Matrix solution of the pentagon equation with anticommuting variables, Teoret. i Matemat. Fizika, 163:3 (2010), 513-528. The authors consider purely mathematical problems of finding an invariant of a 3-manifold and finding certain identities. I tried to present in a clear way the statement of Theorem 1 and main definition from that paper. I bear no responsibility for results of that paper.