
Re: name for definition in group theory
Posted:
Mar 24, 2013 5:03 PM


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 nontrivial 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 nonAbelian, then it has nontrivial inner automorphisms x > (a^(1))xa. Therefore it's Abelian, so x > x^(1) is an automorphism, etc., as you showed.
Ken Pledger.

