References for (especially two-dimensional) general linear groups over *finite* fields
Questions. What are good, citable, detailed sources on general linear groups over finite fields? Especially, GL2(Fp)
, and most especially, the following:
characterization of normalizers of tori in GL2(Fp)
, (I am sorry, but I can't get more specific about this rather special concern, for I want to play by the conventional rules of the reviewing process and not identify myself too much.)
detailed classification of when an element A∈GL2(Fp)
is diagonalizable. There seem to be detailed results on what field-extensions of Fp
the eigenvalues of diagonalizable A∈GL2(Fp)
can possibly lie in (this I infer from the assertions I have to check), but within the time I took during a reviewing job, I did not find a good reference. Algebraically closed fields dominate the literature, needless to say,
characterization of all elements of PGL(2,Fp)
which have order equal to p
,
classification of the intersection of two distinct tori in GL2(Fp)
.
Remarks. Motivation for this reference requestion is that---in a mostly combinatorial article that I am tasked with reviewing---on one page, all of a sudden, I am confronted is a barrage of non-trivial (though no doubt known to experts) assertions about general linear groups over finite fields. (They are using these statements en route to another result.) It is strange, and somewhat reproachable, that the authors do not give a single reference for their statements, writing as if this was an article in a professional algebra journal.
Had I known this, I might have declined this reviewing job, but when I first skimmed the paper, I decided based on the main topic of the paper, and I did not see what was in store for me.
, and most especially, the following:
characterization of normalizers of tori in GL2(Fp)
, (I am sorry, but I can't get more specific about this rather special concern, for I want to play by the conventional rules of the reviewing process and not identify myself too much.)
detailed classification of when an element A∈GL2(Fp)
is diagonalizable. There seem to be detailed results on what field-extensions of Fp
the eigenvalues of diagonalizable A∈GL2(Fp)
can possibly lie in (this I infer from the assertions I have to check), but within the time I took during a reviewing job, I did not find a good reference. Algebraically closed fields dominate the literature, needless to say,
characterization of all elements of PGL(2,Fp)
which have order equal to p
,
classification of the intersection of two distinct tori in GL2(Fp)
.
Remarks. Motivation for this reference requestion is that---in a mostly combinatorial article that I am tasked with reviewing---on one page, all of a sudden, I am confronted is a barrage of non-trivial (though no doubt known to experts) assertions about general linear groups over finite fields. (They are using these statements en route to another result.) It is strange, and somewhat reproachable, that the authors do not give a single reference for their statements, writing as if this was an article in a professional algebra journal.
Had I known this, I might have declined this reviewing job, but when I first skimmed the paper, I decided based on the main topic of the paper, and I did not see what was in store for me.
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