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...
متن کاملNormal Subgroups of the Modular Group Which Are Not Congruence Subgroups
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...
متن کاملComputing with subgroups of the modular group
We give several algorithms for finitely generated subgroups of the modular group PSL2(Z), given by sets of generators. First, we present an algorithm to check whether a finitely generated subgroup H has finite index in the full modular group. Then we discuss how to parametrise the right cosets of H in PSL2(Z), whether the index is finite or not. Further, we explain how an element in H can be wr...
متن کاملCongruence Subgroups of the Modular Group
The congruence subgroups of the classical modular group which can be defined as the automorphs modulo q of some fixed matrix are studied, and their genera determined. Let T = SL{2, Z). A congruence subgroup of T is any subgroup containing a principal congruence subgroup T^), defined as the set of elements A of T such that A = I mod q, where q is a positive integer. Of these one of the most impo...
متن کاملMaximal Nonparabolic Subgroups of the Modular Group
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: Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences
سال: 1970
ISSN: 0098-8979
DOI: 10.6028/jres.074b.012