I am thankful to Marty Isaacs, Witek and Petr Savicky for their valuable
comments on the problem. As pointed out by Marty Isaacs, the question was
looking a homework problem apparently but I was more interested in its solution
in the general form and in the gap function provided there for this purpose.
Petr Savicky ,in a private response to me checked the function to be correct.
He provided me with a much more efficient and fast version of it.
Cheers,
Muhammad Shah
> From: isa...@math.wisc.edu
> To: shahmaths_prob...@hotmail.com
> CC: group-pub-fo...@lists.maths.bath.ac.uk
> Date: Tue, 28 Jun 2016 20:25:39 +0000
> Subject: Re: [group-pub-forum] How to find some special automorphisms?
>
> Your question sounds very much like a homework
> problem, so I will not give much detail in my answer.
>
> Your group G has just two automorphisms: the
> identity and the map that carries every element
> to its inverse. Obviously, the identity automorphism
> fixes all elements of G, and the nonidentity
> automorphism fixes exactly two elements.
>
> Marty Isaacs
>
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