Re: Connected components of a Lie group

From: Maarten Bergvelt (bergv_at_math.uiuc.edu)
Date: 09/20/04 

Date: 20 Sep 2004 14:45:01 -0400

In article <cin6n6$5vv$1@dizzy.math.ohio-state.edu>, Mark Adams wrote:
>
> OK, one more dumb question on Lie groups: the identity component G_e of
> any Lie group G is normal, and the quotient G/G_e is a finite group.
> Since I never see G written as a semidirect product of G_e and G/G_e, I
> assume there must be Lie groups where G/G_e is not isomorphic to a
> finite subgroup of G. Can anyone provide an example of this?

Well, if you take G=G_e\times Z, a countable infinite number of copies
of G_e, the quotient is not finite. Maybe that is not the kind of
example you had in mind... 

-- 
Maarten Bergvelt