Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  247.20008
Autor:  Erdös, Paul; Turan, P.
Title:  On some problems of a statistical group theory. VII. (In English)
Source:  Period. Math. Hung. 2, 149-163 (1972).
Review:  [Part V in Periodica math. Hungar. 1, 5-13 (1971; Zbl 223.10005); Part VI in J. Indian math. Soc., n. Ser. 34 (1970), 175-192 (1971; Zbl 235.10008)]. Denote by Sn the symmetric group of n letters. It is well known that Sn has p(n) conjugacy classes where p(n) is the number of unrestricted partitions of n. The authors prove that for all but O(p(n)) of these conjugacy classes the order O(K) of the elements in the conjugacy class satisfies the inequality

\exp{(A0- \epsilon) \sqrt n} < O(K) < \exp{(A0+\epsilon) \sqrt n}

where A0 = {2 \sqrt 6 \over \pi} sumj \ne 0{(-1)j+1 \over 3j2+j}.
Classif.:  * 20B99 Permutation groups
                   11K99 Probabilistic theory
                   00A07 Problem books

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