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
Annin, Scott and Ziebarth, Jennifer, "Counting Order Classes of Triple Products in Finite Groups" (1994). Mathematical Sciences Technical Reports (MSTR). 122.