Four non - abelian groups of order p 4 as Galois groups ✩
نویسنده
چکیده
Let p be an odd prime and let F be arbitrary field of characteristic not p, containing a primitive pth root of unity ζ . In this paper, we prove a criterion, giving the obstructions to realizability of p-groups as Galois groups over F , having a factor-group of the kind H ×Cp . We apply this to the non-abelian groups of orders p3 and p4. Where it is possible, we give a description of all Galois extensions realizing these groups. We discuss also automatic realizations and local fields. © 2006 Elsevier Inc. All rights reserved.
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