Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 385.20045
Autor: Erdös, Paul; Hall, R.R.
Title: Some new results in probabilistic group theory. (In English)
Source: Comment. Math. Helv. 53, 448-457 (1978).
Review: Let G be an Abelian group of n elements. Assume that for each fixed l the number of elements of order l is o(n) as n ––> oo. Let k = \frac{log n}{log 2}+0(1). Choose k elements of G at random. Let these elements be g1,...,gk and denote by R(g) the number of solutions of g = sumi = 1k\epsilonigi,\epsiloni = 0 or 1. Denote finally by d(r) the number of elements of G with R(g) = r. The authors prove (among others) that of reach fixed r d(r) = (1+0(1))n e-lambda\lambda = \frac{2k}n, with probability tending to 1 as n ––> oo. Several applications and unsolved problems are discussed.
Classif.: * 20P05 Probability methods in group theory
20D99 Abstract finite groups
20K99 Abelian groups
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag