Neil's already answered this, but it brings up an interesting general question: Suppose that you're given a finite group G via black-box. That is you're given its order, n. There's a black box which you can query by giving it a pair of indices between 1 and n and gives back the index of their product (and perhaps you're told that element, 1, say is the identity, and perhaps given an oracle for the inverse). What's the most efficient algorithm to identify the isomorphism class of the group, where the efficiency might be measured in how many queries you need to make? Victor On Mon, Sep 6, 2010 at 2:34 PM, Marc LeBrun <mlb@well.com> wrote:
Can any of you please tell me the name of this pretty group?
0 1 2 3 4 5 6 7 1 0 4 5 2 3 7 6 2 4 0 6 1 7 3 5 3 5 6 0 7 1 2 4 4 2 1 7 0 6 5 3 5 3 7 1 6 0 4 2 6 7 3 2 5 4 0 1 7 6 5 4 3 2 1 0
What do you think would be the best way of answering similar queries?
Thanks! --MLB
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