We classify the nilpotent finite groups G which are such that the unit group ลฝ . U U ZG of the integral group ring ZG has a subgroup of finite index which is the direct product of noncyclic free groups. It is also shown that nilpotent finite groups having this property can be characterised by means
The Normalizer of a Group in the Unit Group of Its Group Ring
โ Scribed by Marcin Mazur
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 127 KB
- Volume
- 212
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We classify all the finite groups G, such that the group of units of ZG contains a subgroup of finite index which is isomorphic to a direct product of nonabelian free ลฝ groups. This completes the work of Jespers, Leal, and del Rฤฑo J. Algebra 180 ลฝ . . 1996 , 22แ40 , where the nilpotent groups with
In the present paper we deal with the canonical projection Pic Z Here p is any odd prime number, `pk k =1 and C n is the cyclic group of order p n . I proved in (Stolin, 1997), that the canonical projection Pic Z[`n] ร Cl Z[`n] can be split. If p is a properly irregular, not regular prime number, t
Let G be an abelian p-group, let K be a field of characteristic different from p, and let KG be the group algebra of G over K. In this paper we give a description ลฝ . ลฝ. of the unit group U KG of KG when i K is a field of the first kind with respect 1 ลฝ . to p and the first Ulm factor GrG is a direc