Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime

We classify compact Riemann surfaces of genus \(g\), where \(g-1\) is a prime \(p\), which have group automorphisms order \(\rho(g-1)\) for some integer \(\rho\ge 1\), and determine isogeny decompositions the corresponding Jacobian varieties. This extends results Belolipetzky second author \(\rho>6\), first third authors \(\rho=\) 3, 4, 5 6. As corollary we orientably regular hypermaps (including maps) \(p+1\), together with non-orientable characteristic \(-p\), automorphism divisible by \(p\); this Conder, Siraň Tucker maps.