On determination of the marks of some alternating groups of small degree (Q799840)

Let g be an integer \(\geq 2\), and denote by \(\ell_ 1\geq\ell_ 2\geq...\geq\ell_ n\geq 1\) the order of the automorphism group A(S) for the various compact Riemann surfaces S of genus g (e.g. \(\ell_ 1=84(g- 1))\). It is known that every finite group is isomorphic to some A(S), with S and g chosen suitably. The author shows that the alternating groups \(A_ 6,A_{10},A_{11},A_{12},A_{13},A_{15}\) are isomorphic to some A(S), with S and g chosen such that the order of A(S) is \(\ell_{\alpha}\), where 1\(\leq\alpha \leq 6\) holds.