Classification of normal subgroups of the modular group
نویسندگان
چکیده
منابع مشابه
Classification of Normal Subgroups of the Modular Group
where a, b, c, d are rational integers and ad-bc= 1. Then T is generated by the linear fractional transformations S, T where St = t+ 1, 7V= — 1/t and is the free product of the cyclic group {T} of order 2 and the cyclic group {ST} of order 3. Let G be a normal subgroup of T of finite index p. It is known that there is just one such subgroup for p=l, 2, 3 which may be described as T", the subgro...
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A subgroup of V containing a principal congruence subgroup T(«) is said to be a congruence subgroup, and is of level « if « is the least such integer. In a recent article [2] the writer determined all normal subgroups of T of genus 1 (see [l] for the definition of the genus of a subgroup of r). An interesting question that arises is to decide which of these are also congruence subgroups. In thi...
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The elliptic elements of M, each with two conjugate complex fixed points, are precisely the conjugates of nontrivial powers of A and B. The parabolic elements, each with a single real fixed point, are precisely the conjugates of nontrivial powers of C = AB: z ~ z + 1. The remaining nontrivial elements of M are hyperbolic, each with two real fixed points. A subgroup S of M is torsionfree (and th...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1967
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1967-0204375-3