Volume 1, 1995, 12 - 21.
Kevin Hutson and Emily Salvo
Conjugacy Classes of Triple Products in Finite Groups

Abstract. Let G be a finite group and let T1 be the number of times a triple xyz binds X={xyz, xzy, yxz, yzx, zxy, zyx} to one conjugacy class. Let T2 denote the number of times a triple breaks X into two conjugacy classes. We have established the following results:

  1. for a random triple xyz so that x, y, and z are in the Dihedral group Dn, the probability that a triple produces one conjugacy class in X is greater than or equal to 5/8.
  2. for groups such that 2|Z(G)||G'|=|G|, T2>=3(|Z(G)|)3|G'|(|G'|-1)2.

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Furman University Electronic Journal of Undergraduate Mathematics