Abstract

Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order lambda(g - 1), for each lambda > 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. (C) 2019 Elsevier Inc. All rights reserved.