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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

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.

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Mathematics Commons

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