## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  235.10008
Autor:  Erdös, Paul; Turán, P.
Title:  On some problems of a statistical group theory. VI. (In English)
Source:  J. Indian Math. Soc., n. Ser. 34 (1970), 175-192 (1971).
Review:  [Part V, Periodica Math. Hungar. 1, 5-13 (1971; Zbl 223.10005).] Let Sn be the symmetric group of n elements, p(n) the number of unrestricted partitions of n. It is well known that there are p(n) conjugacy classes in Sn. Denote by O(H) the order of the elements of Sn in the conjugacy class O(H). Let \omega (n) tend to infinity arbitrarily slowly. The authors prove that for all but o(p(n)) classes H, O(H) is divisible by all primes p not exceeding

{2 \pi \over \sqrt 6}{\sqrt n \over log n} (1+{5 log log n \over log n}-{\omega (n) \over log n} ) .

They also show that the result is best possible.
Classif.:  * 11N60 Distribution functions (additive and positive multipl. functions)
00A07 Problem books
Citations:  Zbl 137.256; Zbl 189.313; Zbl 235.20003; Zbl 235.20004; Zbl 223.10005

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