Newsgroups: sci.math,alt.algebra.help
From: pmontgom@cwi.nl (Peter L. Montgomery)
Subject: Re: infinite groups
Nntp-Posting-Host: bark.cwi.nl
Date: Mon, 20 Jul 1998 09:55:11 GMT

In article <35B30225.100266E3@pottsville.infi.net> 
domm@pottsville.infi.net writes:

>I need assistance with a groups problem and it's not homework.

>What's an example of an infinite group having all elements of finite
>order?

>More than one example would do better.

       The rational numbers modulo 1, under addition.  
If r1/r2 is a rational number in lowest terms, the element has order r2.

       Another example is the additive group of polynomials
modulo a prime p.  Every nonzero polynomial has order p.

       For a non-abelian example, consider all bijections f: Z+ -> Z+
(Z+ = positive integers) such that f(n) = n for all sufficiently 
large n.  If f(n) = n for all n > N, then f permutes
{1, 2, ..., N-1}, and its order divides (N-1)!.

-- 
        Peter-Lawrence.Montgomery@cwi.nl    San Rafael, California