Thinness of some hypergeometric groups in Sp(6)

Abstract: We show that the hypergeometric groups corresponding to the seven pairs of the parameters $\alpha$, $\beta$ where $\alpha$ = (0, 0, 0, 0, 0, 0) and $\beta$ is any of the parameters (1/2, 1/2, 1/2, 1/2, 1/2, 1/2), (1/2, 1/2, 1/2, 1/2, 1/3, 2/3), (1/2, 1/2, 1/2, 1/2, 1/4, 3/4), (1/2, 1/2, 1/2, 1/2, 1/6, 5/6), (1/2, 1/2, 1/3, 2/3, 1/3, 2/3), (1/2, 1/2, 1/3, 2/3, 1/4, 3/4), (1/2, 1/2, 1/5, 2/5, 3/5, 4/5) are thin.