Abstract

Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order λ(g−1), for each λ>6, under the assumption that g−1 is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting 5(g−1) and 6(g−1) automorphisms, with g−1 a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order 3(g−1), with g−1 a prime number. We also provide isogeny decompositions of their Jacobian varieties.