From: David C. Ullrich Subject: Re: Homomorphisms of a finite group Date: Thu, 08 Feb 2001 17:02:21 GMT Newsgroups: sci.math Summary: Pontryagin duality: duals of locally compact abelian groups. In article <95uh9l$tss$1@nnrp1.deja.com>, tim_brooks@my-deja.com wrote: > Let G be a finite group and T the circle group, i.e the complex numbers > z with |z|=1 under complex multiplication. > > what is known about hom(G,T), the Abelian group of group homomorphisms > from G to T ? If G is abelian then hom(G,T) is large enough to separate points of G. In fact if G is abelian and just locally compact (possibly infinite) then the _continuous_ members of hom(G,T) form a thing called the dual group G*; turns out that G* also has a natural locally compact topology and G**=G. This is the Pontryagin(?) duality theorem. I happen to know that even though I know no algebra because it's where abstract "harmonic analysis" starts. If G is not abelian I imagine that in general hom(G,T) can be trivial - don't quote me on that, though. > Thanks, > Tim > > Sent via Deja.com > http://www.deja.com/ > -- Oh, dejanews lets you add a sig - that's useful... Sent via Deja.com http://www.deja.com/