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Topic: name for definition in group theory
Replies: 15   Last Post: Mar 26, 2013 11:35 AM

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Ken.Pledger@vuw.ac.nz

Posts: 1,380
Registered: 12/3/04
Re: name for definition in group theory
Posted: Mar 24, 2013 5:03 PM
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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.



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