Conjugacy Classes of Triple Products in Finite Groups

Authors

Emily Salvo, Villanova University
Kevin Hutson, Clemson University

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) ∈ D³_n 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

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.

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