Sanov subgroup in SL(2,Z)
This article is about a particular subgroup in a group, up to equivalence of subgroups (i.e., an isomorphism of groups that induces the corresponding isomorphism of subgroups). The subgroup is (up to isomorphism) free group:F2 and the group is (up to isomorphism) special linear group:SL(2,Z) (see subgroup structure of special linear group:SL(2,Z)).
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The subgroup has index in the whole group. In fact, any finite index free subgroup of rank two in the special linear group of degree two must have index .