Unramified extensions over low degree number fields
نویسندگان
چکیده
منابع مشابه
Unramified Quaternion Extensions of Quadratic Number Fields
The first mathematician who studied quaternion extensions (H8-extensions for short) was Dedekind [6]; he gave Q( √ (2 + √ 2)(3 + √ 6) ) as an example. The question whether given quadratic or biquadratic number fields can be embedded in a quaternion extension was extensively studied by Rosenblüth [32], Reichardt [31], Witt [36], and Damey and Martinet [5]; see Ledet [19] and the surveys [15] and...
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Consider the set of number fields unramified away from 2, i.e., unramified outside {2,∞}. We show that there do not exist any such fields of degrees 9 through 15. As a consequence, the following simple groups are ruled out for being the Galois group of an extension which is unramified away from 2: Mathieu groups M11 and M12, PSL(3, 3), and alternating groups Aj for 8 < j < 16 (values j ≤ 8 were...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2020
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.10.021