subgroups of SL - sci.math

Message from discussion subgroups of SL

leiko

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More options Nov 3 2009, 3:47 pm

Newsgroups: sci.math

From: leiko <leikomats...@gmail.com>

Date: Tue, 3 Nov 2009 07:47:33 -0800 (PST)

Local: Tues, Nov 3 2009 3:47 pm

Subject: Re: subgroups of SL

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On Nov 3, 6:22 am, José Carlos Santos <jcsan...@fc.up.pt> wrote:

> On 03-11-2009 6:46, leiko wrote:

> > Why is a finite subgroup of SL (2,R) cyclic?

> Every finite subgroup of SL(2,R) is isomorphic to a finite subgroup of
> the group of all rotations of R^2. Since this is just S^1, it is easy to
> prove that such a group is cyclic.

> Best regards,

> Jose Carlos Santos

Thanks a lot for your replies. The Sl(3,r) example is neat.

About Sl(2,r) - the group of rotations is SO(2,r), and this is just a
subgroup of Sl(2,r), am I right?
I think I can show that So(2,r) is isomorphic to S^1, but how can i
show that a finite subgroup of Sl(2,r) is in fact a subgroup of So
(2,r)?

Thanks a lot again.

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