The 2-class group of biquadratic fields. II

The Generators of the 2-class Group of Some Fields

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

An explicit treatment of biquadratic function fields

We provide a comprehensive description of biquadratic function fields and their properties, including a characterization of the cyclic and radical cases as well as the constant field. For the cyclic scenario, we provide simple explicit formulas for the ramification index of any rational place, the field discriminant, the genus, and an algorithmically suitable integral basis. In terms of computa...

The structure of some 2-groups and the capitulation problem for certain biquadratic fields

We study the capitulation problem for certain number fields K of degree 4 and we show how we can determine the structures of some 2-groups as an application of this study. Let K (2) 1 be the Hilbert 2-class field of K, K (2) 2 be the Hilbert 2-class field of K (2) 1 , CK,2 be the 2component of the ideal class group of K and G2 the Galois group of K (2) 2 /K. We suppose that CK,2 is of type (2, ...

The 4-class Group of Real Quadratic Number Fields

In this paper we give an elementary proof of results on the structure of 4-class groups of real quadratic number fields originally due to A. Scholz. In a second (and independent) section we strengthen C. Maire’s result that the 2-class field tower of a real quadratic number field is infinite if its ideal class group has 4-rank ≥ 4, using a technique due to F. Hajir.