Fields, Matrix Groups and p-Sylow Subgroups
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Consider the field F_7 ~/= Z/7Z having 7 elements, and consider the matrix group:
G= {(t s) |t E F(^x)(_7), x E F_7}.
.......(0 t^(-1))
Find all Sylow 3-subgroups of G. Can you find a "systematic" way of describing them?
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