Subgroups of infinite index in the modular group II
نویسندگان
چکیده
منابع مشابه
Subgroups of Small Index in Infinite Symmetric Groups II
Throughout this paper Q will denote an infinite set, S:= Sym(Q) and G is a subgroup of S. If n: = |Q|, the cardinal of Q, then |.S| = 2". Working in ZFC, set theory with Axiom of Choice (AC), we shall be seeking the subgroups G with \S: G\ < 2". If A £ Q then S^ (respectively G{A}) denotes the setwise stabiliser of A in S (respectively in G); 5(A) and G(A) denote pointwise stabilisers; we ident...
متن کاملFinite Index Subgroups of the Modular Group and Their Modular Forms
Classically, congruence subgroups of the modular group, which can be described by congruence relations, play important roles in group theory and modular forms. In reality, the majority of finite index subgroups of the modular group are noncongruence. These groups as well as their modular forms are central players of this survey article. Differences between congruence and noncongruence subgroups...
متن کاملClosed subgroups of the infinite symmetric group
Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪U 〉 = 〈G2 ∪U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on which ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1981
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500004523