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On projective linear groups over finite fields as Galois groups over the rational numbers

Gabor Wiese
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Abstract

Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l, the infinite place and only one other prime.

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Gabor Wiese. 2007-11-21. On projective linear groups over finite fields as Galois groups over the rational numbers. https://arxiv.org/abs/math/0606732

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