##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 223.10005

**Autor: ** Erdös, Paul; Turán, P.

**Title: ** On some problems of a statistical group theory. V. (In English)

**Source: ** Period. Math. Hung. 1, 5-13 (1971).

**Review: ** [Part IV, Acta math. Acad. Sci. Hungar. 19, 413-435 (1968; Zbl 235.20004).]

Let S_{n} be the symmetric group of n elements. It is well known that the number of conjugacy classes of S_{n} is p(n) the number of partitions of n. Let H be an element of S_{n} O(H) its orders which only depends on the conjugacy class of H. P(H) denotes the greatest prime factor of O(H). The authors prove the following theorem: For almost all H (i.e. for all H except for o(p(n)) of them) we have |P(H)-**(**{\sqrt{6n} \over 2 \pi} log n-{\sqrt{6n} \over \pi} log log n **)**| < \omega (n) \sqrt n where \omega(n) tends to infinity as slowly as we please. [See also the authors, Acta. Math. Acad. Sci. Hung. 18, 151-163 (1967; Zbl 189.31302).]

**Classif.: ** * 11P82 Analytic theory of partitions

20P05 Probability methods in group theory

05A17 Partitions of integres (combinatorics)

20B35 Subgroups of symmetric groups

20B30 General theory of symmetric groups

00A07 Problem books

**Citations: ** Zbl 235.20004; Zbl 235.20003

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag