Let G be an abelian group with n elements, and let {g1=e,g2,…,gk}⊊G be a (not necessarily minimal) set of distinct generators of G. A special die, which randomly selects one of the elements g1,g2,…,gk with equal probability, is rolled m times and the selected elements are multiplied to produce an element g∈G.Prove that there exists a real number b∈(0,1) such that m→∞limb2m1x∈G∑(Prob(g=x)−n1)2 is positive and finite. Putnamabstract algebraprobabilitylimitreal analysislinear algebramatrix