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.
Professor Jorge Morales, Professor of Mathematics, Louisiana State University
Burdick, Bradley Lewis and Jonker, Jonathan
"Generic Polynomials for Transitive Permutation Groups of Degree 8 and 9,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 9.
Available at: http://scholar.rose-hulman.edu/rhumj/vol14/iss1/9