کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593557 1630662 2015 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Classes réalisables d'extensions non abéliennes de degré p3
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Classes réalisables d'extensions non abéliennes de degré p3
چکیده انگلیسی
Let k be a number field and Ok its ring of integers. Let p be an odd prime number. Let Γ be a non-abelian group of order p3. Let M be a maximal Ok-order in the semi-simple algebra k[Γ] containing Ok[Γ], and let Cl(M) be its locally free classgroup. We define the set R(M) of realizable classes to be the set of classes c∈Cl(M) such that there exists a Galois extension N/k which is tame, with Galois group isomorphic to Γ, and for which the class of M⊗Ok[Γ]ON is equal to c, where ON is the ring of integers of N. Let ξ (resp. ξp2) be a primitive pth (resp. p2th) root of unity. In the present article, under the hypothesis that k/Q and Q(ξ)/Q are linearly disjoint and k(ξp2)/k(ξ) is not ramified when Γ has exponent p2, we define a subset of R(M) by means of a Stickelberger ideal, and prove that it is a subgroup of Cl(M) contained in R(M).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 152, July 2015, Pages 55-89
نویسندگان
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