Note on 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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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 کاملA Note on Subgroups of the Modular Group1
8. M. Nakaoka and H. Toda, On Jacobi identity for Whitehead products, J. Inst. Polytech. Osaka City Univ. Ser. A. 5 (1954), 1-13. 9. J.-P. Serre, Groupes d'homotopie et classes de groupes abéliens, Ann. of Math. (2) 58 (1953), 258-294. 10. N. Shimada, Triviality of the mod p Hopf invariants, Proc. Japan Acad. 36 (1960), 68-69. 11. N. E. Steenrod, Cohomology invariants of mappings, Ann. of Math....
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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...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1966
ISSN: 0002-9939
DOI: 10.2307/2036118