Computation of Locally Free Class Groups

نویسندگان

  • Werner Bley
  • Robert Boltje
چکیده

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Results on Engel Fuzzy Subgroups

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

متن کامل

On trivial ends of Cayley graph of groups

‎In this paper, first we introduce the end of locally finite graphs as an equivalence class of infinite paths in the graph. Then we mention the ends of finitely generated groups using the Cayley graph. It was proved that the number of ends of groups are not depended on the Cayley graph and that the number of ends in the groups is equal to zero, one, two, or infinity. For ...

متن کامل

On continuous cohomology of locally compact Abelian groups and bilinear maps

Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

متن کامل

Topology Proceedings 45 (2015) pp. 175-187: Topological entropy for automorphisms of totally disconnected locally compact groups

We give a “limit-free formula” simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend to our setting several basic properties of the topological entropy known for compact groups.

متن کامل

Capitulation for Locally Free Class Groups of Orders of Group Algebras over Number Fields

We prove a capitulation result for locally free class groups of orders of group algebras over number fields. This result allows some control over ramification and so as a corollary we obtain an “arithmetically disjoint capitulation result” for the Galois module structure of rings of integers.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2006