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?(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Finding non-trivial automorphisms of large Abelian groups

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