Date: Mar 24, 2013 5:03 PM
Subject: Re: name for definition in group theory
In article <email@example.com>,
David C. Ullrich <firstname.lastname@example.org> wrote:
> On Sun, 24 Mar 2013 08:15:15 -0700 (PDT), Paul <email@example.com>
> >Does anyone know the name for the following property of a group G: G has
> >no non-trivial automorphisms. ?
> >Thank you
> These groups are referred to as "groups of order 1 or 2".
> There must be a very elementary proof of this. I know
> no group theory; here's a not quite elementary proof
> using a big result from harmonic analysis....
If G is non-Abelian, then it has non-trivial inner automorphisms
x -> (a^(-1))xa. Therefore it's Abelian, so x -> x^(-1) is an
automorphism, etc., as you showed.