Title

Commuting Pairs in Finite Non-Abelian Groups

Date

5-26-2016 10:30 AM

End Time

26-5-2016 10:45 AM

Location

MNB 104

Department

Mathematics

Session Chair

Matthew Nabity

Session Title

Mathematics Senior Project Presentations

Faculty Sponsor(s)

Mike Ward

Abstract

The study of the probability that two group elements commute dates back to 1968 with the work of Paul Erdos and Paul Turan. Since then, much has been deduced about these probabilities, including its bound of 5/8. During this talk, we will look at the associated probabilities of finite non-abelian groups and how to calculate such probabilities using several methods. When calculating specific probabilities, we will look at the conjugacy classes associated with these groups which will reveal the relationship that conjugacy has to commutativity. Next, we will explore the probabilities associated with Dihedral groups and how to calculate probabilities with specific denominators as well as specific numerators. We will also look at the group of GL(2,Zp) matrices and deducing the probability that two of these matrices commute. Finally, we will wrap up with looking into some further research on this topic including some of the bounds associated with Dihedral groups.

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May 26th, 10:30 AM May 26th, 10:45 AM

Commuting Pairs in Finite Non-Abelian Groups

MNB 104

The study of the probability that two group elements commute dates back to 1968 with the work of Paul Erdos and Paul Turan. Since then, much has been deduced about these probabilities, including its bound of 5/8. During this talk, we will look at the associated probabilities of finite non-abelian groups and how to calculate such probabilities using several methods. When calculating specific probabilities, we will look at the conjugacy classes associated with these groups which will reveal the relationship that conjugacy has to commutativity. Next, we will explore the probabilities associated with Dihedral groups and how to calculate probabilities with specific denominators as well as specific numerators. We will also look at the group of GL(2,Zp) matrices and deducing the probability that two of these matrices commute. Finally, we will wrap up with looking into some further research on this topic including some of the bounds associated with Dihedral groups.