## Furman University Electronic Journal of Undergraduate Mathematics

### Volume 1, 1995.

**Kevin Hutson and Emily Salvo**

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:
- 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
- for groups such that 2|Z(G)||G'|=|G|, T2>=3(|Z(G)|)^3|G'|(|G'|-1)^2.

Volume One Contents

Furman University Electronic Journal of Undergraduate
Mathematics