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 Apr21 comment How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases? @ahorn That's a good point, Indeed my choice was arbitrary. I edited my answer to reflect this. Mar16 comment Finite field question involving the trace and a permutation. Many thanks Jyrki, I'll need to study this a bit. I'll update later. Mar16 comment Finite field question involving the trace and a permutation. I know a couple of people who were claiming that they could do math better after a couple of beers :) Anyway, I think I have an idea, but I have to double think before posting anything, I'm not sure yet. Mar10 comment Bijections of a finite field that preserve the kernel of the trace I have realized what my $f(x)$ should be. Indeed, I was asking too much. If you want, check my updated question here: math.stackexchange.com/questions/1183155/… Feb24 comment Bijections of a finite field that preserve the kernel of the trace Thank you for your clear and thorough answer, I was quite off with my conjecture about these monomials. I will have to think how/if the question can be restated to suggest some other class of polynomials. Feb24 comment Bijections of a finite field that preserve the kernel of the trace I think I was being quite careless when I wrote that title. It should be just bijections. Jul7 comment Which powers of a primitive element of a finite field yield a generator of a finite field extension? Thanks for your answer. Now, you say that WLOG, $i|(q^m-1)$, else $i$ is associate to a divisor's residue in $\Bbb{Z}_{q^m-1}$. Could you comment on that? I fail to understand it.. Jul4 comment Which powers of a primitive element of a finite field yield a generator of a finite field extension? Note that the last bullet is equivalent to "there is no $s$ such that \$0