## 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 Sn be the symmetric group of n elements. It is well known that the number of conjugacy classes of Sn is p(n) the number of partitions of n. Let H be an element of Sn 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

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