On the Power Subgroups of the Extended Modular Group \overline{G} (Corrigendum - Turk. J. Math. 28,143-151, 2004)
In [1], we proved that, if N is a non-trivial normal subgroup of Γ different from Γ, Γ, Γ2, Γ3, then N is a free group. When we were doing this proof, we used the fact that an element of order 2 in Γ is conjugate to T or to R and an element of order 3 in Γ is conjugate to a power of S. But while determining some low indexed normal subgroups of the extended modular group, we found two non-free normal subgroups of the extended modular group Γ having index 2 (except for the modular group Γ) and a non-free normal subgroup of the extended modular group having index 6 (except for the subgroup Γ3). Also, when we were investigating conjugacy classes of finite order elements in Γ (see [2]), we determined a conjugacy class of reflection with representative T R, except the other conjugacy class of reflection with representative R. Thus we want to restate results related free normal subgroups of the extended modular group Γ, specificially (the lemma 3.2, theorem 3.3 and theorem 3.4).
On the Power Subgroups of the Extended Modular Group \overline{G}
In [1], we proved that, if N is a non-trivial normal subgroup of Γ different from Γ, Γ, Γ2, Γ3, then N is a free group. When we were doing this proof, we used the fact that an element of order 2 in Γ is conjugate to T or to R and an element of order 3 in Γ is conjugate to a power of S. But while determining some low indexed normal subgroups of the extended modular group, we found two non-free normal subgroups of the extended modular group Γ having index 2 (except for the modular group Γ) and a non-free normal subgroup of the extended modular group having index 6 (except for the subgroup Γ3). Also, when we were investigating conjugacy classes of finite order elements in Γ (see [2]), we determined a conjugacy class of reflection with representative T R, except the other conjugacy class of reflection with representative R. Thus we want to restate results related free normal subgroups of the extended modular group Γ, specificially (the lemma 3.2, theorem 3.3 and theorem 3.4).
