Counting Order Classes of Triple Products in Finite Groups
Scott A. Annin, Jennifer Ziebarth · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 1994
Let G be a finite group and let WG denote the proportion of triples, (.x:, y , z) , i n G3 for which x yz , x zy, y x z, zx y , yzx , and z y x have the same order. The following results are established. i) G is abelian if, and only if, WG = 1. ii) WG can be arbitrarily close to 1. iii) Additional estimates on WG