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