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Generalizing the modular and Hecke groups, we consider the subgroup Π of SL(2, ℤ[
ξ
]) generated by the parabolic element
and the elliptic element
, where ℤ[
ξ
] is the ring of polynomials in the variable
ξ
. For
ζ
∈ ℂ and
W
∈ Π, we denote by
W
(
ζ
) the matrix in SL(2, ℂ) obtained when evaluating the parameter
ξ
at
ζ
. We enumerate the elements of Π and study the relators, defined as those
W
∈ ℂ for which there exists
ζ
∈ ℂ with
W
(
ζ
) = ±
I
. Then, for
W
∈ Π, we investigate the sets of
ζ
for which
W
(
ζ
) is not loxodromic; their union is the singular set
S
(Π) ⊂ ℂ. The closure of the singular set for the two-parabolic group, which is isomorphic to a free subgroup Π of index 4, has been studied extensively.