///////////////////////////////////////////////////////////////////////////
// "Growth of torsion groups of elliptic curves upon base changes"
// Enrique González-Jiménez & Filip Najman
///////////////////////////////////////////////////////////////////////////

// 13/10/2016 - Magma 2.21

// Magma script related to Proposition 8.1


// GL(2,3) has no subgroups isomorphic to S_4:

G:=GL(2,3);
S4:=Group("S4");
[ IsIsomorphic(S4,H`subgroup): H in Subgroups(G) | Index(G,H`subgroup) eq 2];

/* OUTPUT: GL(2,3) has no subgroups isomorphic to S_4

[ false ]

*/