Article Title
Abstract
Let G be a finite group and let T1 be the number of times a triple (x, y, z) ∈ G3 binds X, where X = {xyz, xzy, yxz, yzx, zxy, zyx}, to one conjugacy class. Let T2 denote the number of times a triple G3 breaks X into two conjugacy classes. We have established the following results: i) the probability that a triple (x, y, z) ∈ D3n binds X to one contingency class is ≥ 5/8. ii) for groups such that 2|Z(G)||G'|=|G|, T2≥3(|Z(G)|)3|G'|(|G'|-1)2.
Faculty Advisor Name
Alice A. Dean
Faculty Advisor Institution
Villanova University
Suggested Mathematics Subject Classification(s)
20B05
Recommended Citation
Emily Salvo and Kevin Hutson, Conjugacy Classes of Triple Products in Finite Groups, Furman University Electronic Journal of Undergraduate Mathematics, 1 (2016), 12-21. Available at: https://scholarexchange.furman.edu/fuejum/vol1/iss1/2
Comments
Both authors supported by NSF Grant NSF–DMS 9322338. Research done at Rose-Hulman Institute of Technology in NSF sponsored REU in Computational Finite Group Theory, under the directorship of Gary Sherman.