On ideal class groups of $2$-power exponent
نویسندگان
چکیده
منابع مشابه
On the rank of ideal class groups
We review some questions of Shafarevich on the structure of ideal class groups of number elds, and discuss results that provide evidence in support of these questions. The analogy between number elds and algebraic function elds of one variable has long been a fruitful source of inspiration for the development of algebraic number theory. Hilbert's pioneering work in class eld theory, for instanc...
متن کاملOn the Exponent of Triple Tensor Product of p-Groups
The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...
متن کاملCOMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2
The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. Th...
متن کاملOn the Structure of Ideal Class Groups of CM - Fields
For a CM-field K which is abelian over a totally real number field k and a prime number p, we show that the structure of the χ-component AχK of the p-component of the class group ofK is determined by Stickelberger elements (zeta values) (of fields containing K) for an odd character χ of Gal(K/k) satisfying certain conditions. This is a generalization of a theorem of Kolyvagin and Rubin. We defi...
متن کاملOn rational groups with Sylow 2-subgroups of nilpotency class at most 2
A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1982
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1982-0667271-7