Theorem I1 I^{+}(2) = M(2)




Lemma For c ε C, I^{+}(2) and M(2) each contain the element j_{c} given by
To see that it is in I^{+}(2), observe that j_{c} = i_{1}or_{0}ot_{c}. The result for M(2) is clear from the formula for j_{c}.


Proof of Theorem I1 We show that each of I^{+}(2) and M(2) is generated by the elements of S^{+}(2) and the j_{c}, so the groups are equal.
From the ∞ Theorem S(2) is the subgroup of I(2) which fixes ∞
Now suppose that tεI^{+}(2) is such that t(∞) = c ≠ ∞.
For M(2), we have a similar argument.
Finally, just as for I^{+}(2), we can show that
