Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 336.20041
Autor: Erdös, Paul; Hall, R.R.
Title: Probabilistic methods in group theory. II. (In English)
Source: Houston J. Math. 2, 173-180 (1976).
Review: [Part I: P. Erdös and A. Rényi, J. Analyse math. 14, 127-138 (1965; Zbl 247.20045).] The authors prove the following theorem: Let G be an abelian group of n elements. Put K = [(1+\epsilon){log n \over log 2} ]. Choose k elements of our group in all possible ways. There the nk ways of choosing the elements x1, ... ,xk. For all but o(nk) choices are number of solutions of prod ki = 1x\epsilonii = g, \epsiloni = 0 or 1 is (1+o(1)){2k \over n} for every element g of G. This theorem settles an old problem of Erdös and Rényi.
Classif.: * 20K99 Abelian groups
11B83 Special sequences of integers and polynomials
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