Generic Polynomials for Transitive Permutation Groups of Degree 8 and 9

Authors

Bradley Lewis Burdick, The Ohio State UniversityFollow
Jonathan Jonker, Michigan State University

Abstract

We compute generic polynomials for certain transitive permutation groups of degree 8 and 9, namely SL(2,3), the generalized dihedral group: C2 \ltimes (C3 x C3), and the Iwasawa group of order 16: M16. Rikuna proves the existence of a generic polynomial for SL(2,3) in four parameters; we extend a computation of Grobner to give an alternative proof of existence for this group's generic polynomial. We establish that the generic dimension and essential dimension of the generalized dihedral group are two. We establish over the rationals that the generic dimension and essential dimension of SL(2,3) and M16 are four.

Author Bio

Bradley Lewis Burdick is an undergraduate at the Ohio State University pursuing a BS in English and Mathematics with a focus in poetry and topology. This research was completed with his participation in Louisiana State University's Mathematics REU. He plans to pursue a PhD in mathematics.

Jonathan Jonker is an undergraduate at Michigan State University. This research was done during an REU funded by the NSF and hosted by LSU. He plans to go to graduate school to pursue a PhD in mathematics.

Faculty Sponsor

Jorge Morale

Recommended Citation

Burdick, Bradley Lewis and Jonker, Jonathan (2013) "Generic Polynomials for Transitive Permutation Groups of Degree 8 and 9," Rose-Hulman Undergraduate Mathematics Journal: Vol. 14: Iss. 1, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss1/9