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Undergraduates, The Right Questions, And Cayley Produce Results, Gary J. Sherman
Undergraduates, The Right Questions, And Cayley Produce Results, Gary J. Sherman
Mathematical Sciences Technical Reports (MSTR)
During the summers of 1989, 1990, and 1991, eighteen undergraduates participated in a National Science Foundation Research Experiences for Undergraduates program at Rose-Hulman for which the author was the principal investigator. This paper provides some examples of the mathematics discovered during these three summers and discusses the philosophy, environment and process which made these discoveries possible.
More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic
More Upper Bounds On The 3-Rewriteability Of Non-3-Rewriteable Groups, Eric Wepsic
Mathematical Sciences Technical Reports (MSTR)
We find an upper bound on the probability that a randomly selected triple in a group is 3-rewriteable, and a bound for the core set rewriteability.
Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic
Cyclicizers, Centralizers, And Normalizers, David Patrick, Eric Wepsic
Mathematical Sciences Technical Reports (MSTR)
Our goal is to define the cyclicizer, which is analogous to the centralizer and normalizer, and to examine groups in which these subsets have certain special properties.
Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman
Counting Centralizers In Finite Groups, Sarah Marie Belcastro, Gary J. Sherman
Mathematical Sciences Technical Reports (MSTR)
We discuss various results on the number of commuting pairs and the sizes of the centralizers of a group.
Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner
Integer Triangles With Rational Medians, Bart Goddard, Dale Mesner
Mathematical Sciences Technical Reports (MSTR)
A characterization of all integer-sided triangles with a rational median is given, similar to the categorization of Pythagorean triangles. An infinite family of integer-sided triangles with two rational medians is given, along with several examples of three rational medians. All examples come from solutions to systems of quadratic Diophantine equations.
An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg
An Upper Bound For 3-Rewriteability In Finite Groups, Jordan Ellenberg
Mathematical Sciences Technical Reports (MSTR)
An ordered triple of group elements (x,y,z) is said to be rewriteable if the product xyz is equal to one of the products xzy, yxz, yzx, zxy, zyx. In the present paper, we shall ask the following question: how rewriteable can a finite group be if its derived group has order greater than 2?
Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman
Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman
Mathematical Sciences Technical Reports (MSTR)
Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G.