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From: Geoff on 17 Mar 2010 18:05
Are all congruence subgroups of SL(2, Z) finite index? Thanks.
From: Tonico on 17 Mar 2010 18:45
On Mar 18, 12:05 am, Geoff <geoffreym...(a)gmail.com> wrote:
> Are all congruence subgroups of SL(2, Z) finite index?  Thanks.


Yes. A congruence subgroup is one that contains G(N), where
1 --> G(N) --> SL(2,Z) --> SL(2,Z/nZ) --> 1 is an exact sequence (G(N)
is the set of matrices reduced modulo N), so G(N) has finite index and
thus any congruence sbgp., as well.

Tonio
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