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Generic Polynomials for Transitive Permutation Groups of Degree 8 and 9

By Of Degree, Bradley Lewis Burdick A, Jonathan Jonker B, Bradley Lewis Burdick and Jonathan Jonker


Abstract. We compute generic polynomials for certain transitive permutation groups of degree 8 and 9, namely SL(2,3), the generalized dihedral group: C2 ⋉ (C3 × C3), and the Iwasawa group of order 16: M16. Rikuna proves the existence of a generic polynomial for SL(2,3) in four parameters in [13]; we extend a computation of Gröbner in [5] 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. Acknowledgements: This work was completed as a part of the Louisiana State University’s 2012 Math REU. The authors would like to thank NSF for funding the REU, Dr. Jorge Morales for guidance and direction, and the referee for referring us to [9] and the idea for Theorems 3.9 and 5.11.Page 114 RHIT Undergrad. Math. J., Vol. 14, No. 1

Year: 2013
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