GALOIS p-GROUPS AND GALOIS MODULES

被引：8
作者：
Chebolu, Sunil [1 ]
Minac, Jan [2 ]
Schultz, Andrew [3 ]
机构：
[1] Illinois State Univ, Dept Math, Campus Box 4520, Normal, IL 61790 USA
[2] Univ Western Ontario, Middlesex Coll, Dept Math, London, ON N6A 5B7, Canada
[3] Wellesley Coll, Dept Math, 106 Cent St, Wellesley, MA 01702 USA
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2016年 / 46卷 / 05期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Galois groups; p-groups; Galois modules; enumerating Galois extensions; norm residue isomorphism; MASSEY PRODUCTS; ZASSENHAUS FILTRATION; CYCLIC EXTENSIONS; COHOMOLOGY; CONJECTURE;
D O I：
10.1216/RMJ-2016-46-5-1405
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups as well as other closely related, larger p-groups occur as Galois groups over given base fields. We show further how the appearance of some Galois groups forces the appearance of other Galois groups in an interesting way.
引用
收藏
页码：1405 / 1446
页数：42
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