Triangular Maps and Non-Congruence Subgroups of the Modular Group

1979 ◽  
Vol 11 (2) ◽  
pp. 117-123 ◽  
Author(s):  
Gareth A. Jones
Keyword(s):  
Modular Group ◽  
Congruence Subgroups ◽  
Triangular Maps

scholarly journals Macbeath's curve and the modular group

1985 ◽  
Vol 27 ◽  
pp. 239-247 ◽  
Author(s):  
K. Wohlfahrt
Keyword(s):  
Finite Index ◽  
Modular Group ◽  
Algebraic Curves ◽  
The Other ◽  
Congruence Subgroups ◽  
Related Research ◽  
Other Hand

The theory of algebraic curves associated with subgroups of finite index in the modular group Γ is highly developed for such subgroups of Γ as may be defined by means of congruences in the ring ℤ of rational integers. The situation in he case of non-congruence subgroups of Γ, on the other hand, is drastically different. It reduces to a few isolated examples, two of which may be found in [12]. Related research by A. O. L. Atkin and H. P. F. Swinnerton-Dyer began in [1].

Level and index in the modular group

1984 ◽  
Vol 99 (1-2) ◽  
pp. 115-126 ◽  
Author(s):  
W. W. Stothers
Keyword(s):  
Modular Group ◽  
Congruence Subgroup ◽  
Existence Theorems ◽  
Congruence Subgroups ◽  
Similar Action

SynopsisIt is shown that the index of a congruence subgroup of the modular group cannot be less than the level of the subgroup. This allows a number of existence theorems about non-congruence subgroups.The level of a subgroup of the modular group can be defined in terms of the action on Q ∪ {∞}. We define a similar action to get information on congruence subgroups. In fact, we get a more powerful result, but this appears to be the most useful version.

Automorphisms and Congruence Subgroups of the Extended Modular Group

1986 ◽  
Vol s2-34 (1) ◽  
pp. 26-40 ◽  
Author(s):  
Gareth A. Jones ◽  
John S. Thornton
Keyword(s):  
Modular Group ◽  
Congruence Subgroups
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