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Finding non-trivial automorphisms of large Abelian groups

  1. May 30, 2015 #1
    I feel there should be a way to find non-trivial (other than ##\operatorname{inn} G##) automorphisms of these groups other than by trial-and-error computation. Take for example ##\operatorname{aut}\mathbb{Z}_{100!}^*## . Are these just computationally inaccessable to us forever?

    How about a simpler task: Now ##1_{G}(\mathbb{Z}_{100!}^*)=\{1,a_2,a_3,\cdots,n-1\}##. What is the least (even) number of substitutions I would have to make to obtain another automorphism? And can I figure that out other than by brute-force computation or is even brute-force searching computationally feasible for this group?

    Or another:

    Find a generator mapping ##\big\{a_1,a_2,\cdots,a_k\big\} \to \big\{b_1,b_2,\cdots,b_k\big\} ## that leads to a non-trivial automorphism other than by trial-and-error computation of residues.

    Are there ways of doing these things for Abelian groups?

    Ok thanks,
    Jack
     
    Last edited: May 30, 2015
  2. jcsd
  3. Jun 4, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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