Our computations show that there is a total of 40 pairs degree six coprime polynomials f,g where f(x)=(x?1)6, g product cyclotomic polynomials, g(0)=1 and form primitive pair. The aim this article to determine whether the corresponding symplectic hypergeometric groups with maximally unipotent monodromy follow same dichotomy between arithmeticity thinness holds for 14 four f(x)=(x?1)4 as describ...

A transitive subgroup G ≤ SN is called a genus zero group if there exist non identity elements x1 , . xr∈G satisfying =<x1, xr>, x1·...·xr=1 and ind x1+...+ind xr = 2N − 2. The Hurwitz space Hinr(G) the of coverings Riemann sphere P1 with r branch points monodromy G.In this paper, we assume that finite PSp(4, q) Aut(PSp(4, q)) acts on projective 3-dimensional geometry PG(3, q), q prime po...

Let R be a commutative ring, and let l ≥ 2; for l = 2 it is assumed additionally that R has no residue fields of two elements. The subgroups of the general linear group GL(n,R) that contain the elementary symplectic group Ep(2l, R) are described. In the case where R = K is a field, similar results were obtained earlier by Dye, King, and Shang Zhi Li. In the present paper we consider a descripti...