TY - JOUR
T1 - Wild ramification bounds and simple group galois extensions ramified only at 2
AU - Jones, John
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2011/3
Y1 - 2011/3
N2 - We consider finite Galois extensions of Qp and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of Q, unramified outside of {2,∞}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.
AB - We consider finite Galois extensions of Qp and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of Q, unramified outside of {2,∞}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.
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U2 - 10.1090/S0002-9939-2010-10628-7
DO - 10.1090/S0002-9939-2010-10628-7
M3 - Article
AN - SCOPUS:79951828914
SN - 0002-9939
VL - 139
SP - 807
EP - 821
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -