Was Galois aware of group GA(1,5)?

Discussion in 'Linear and Abstract Algebra' started by Stedman, Apr 19, 2020.

  1. Stedman


    Apr 19, 2020
    Likes Received:
    The general affine group of order 20 was used by a Change Ringing composer for a peal composition at some point between 1832 and 1842. Group Theory is fundamental to Change Ringing, and the group Sn is often rung on numbers of bells between 4 and 7. Thus, there are many subgroups of Sn that are well-known to ringing composers, who use them to construct compositions.

    My question is: was Galois aware of GA(1,5)? (Also known as F20). I believe he classified finite subgroups on 5 integers, so it seems likely that he did know of the group. If so, he would only just have been the first to discover it - considering that he died in 1832 at the untimely age of 20 - and the change ringing composer, John Lates, produced his composition sometime between 1832 - 42 (probably nearer 1842.)
    Stedman, Apr 19, 2020
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