Date: Mar 24, 2013 5:03 PM
Author: Ken.Pledger@vuw.ac.nz
Subject: Re: name for definition in group theory
In article <m89uk8lshngii7afp7qktplg90ubnq9doj@4ax.com>,

David C. Ullrich <ullrich@math.okstate.edu> wrote:

> On Sun, 24 Mar 2013 08:15:15 -0700 (PDT), Paul <pepstein5@gmail.com>

> wrote:

>

> >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.

Ken Pledger.