### 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 T_{1} be the number of
times a triple *xyz* binds X={*xyz, xzy, yxz, yzx, zxy, zyx*}
to one conjugacy class. Let T_{2} denote the number of times a triple breaks
X into two conjugacy classes. We have established the following results:
- for a random triple
*xyz* so that *x*, *y*, and *z*
are in the Dihedral group D_{n}, the probability that a triple produces one
conjugacy class in X is greater than or equal to 5/8.
- for groups such that 2|Z(G)||G'|=|G|, T
_{2}>=3(|Z(G)|)^{3}|G'|(|G'|-1)^{2}.

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Furman University Electronic Journal of Undergraduate Mathematics