On the order of a random permutation

Let $S_n$ be a group of permutations of a set with $n$ elements. In the report, the so-called general parametrical model of random permutation (r.p.) is considered. According to it, each cycle of any fixed permutation from $S_n$ possesses (generally speaking, non-negative) weight depending on its length. For properly centered and normalized of logarithm of an order of r.p. in this model, the limit theorem of weak convergence to the normal law is received. At the beginning of the report, the small review of the most interesting previous results in this direction, since P. Erdős and P. Turán's fundamental work of 1965 will be made. Any prior knowledge from this area isn't required, the main used notion is the permutation which is known, for example, to students, from the course of linear algebra or from the theory of finite groups.