Group rings of finite strongly monomial groups: Central units and primitive idempotents

JOURNAL OF ALGEBRA

卷:387

Article

Jespers, Eric¹  Olteanu, Gabriela²  del Rio, Angel³  Van Gelder, Inneke¹ 

[1] Vrije Univ Brussel, Dept Math, B-1050 Brussels, Belgium

[2] Univ Babes Bolyai, Dept Stat Forecast & Math, Cluj Napoca 400591, Romania

[3] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

关键词: Group rings;    Central units;    Generators;    Orthogonal primitive idempotents;   

DOI  :  10.1016/j.jalgebra.2013.04.020

来源: Elsevier

【 摘 要 】

We compute the rank of the group of central units in the integral group ring ZG of a finite strongly monomial group G. The formula obtained is in terms of the strong Shoda pairs of G. Next we construct a virtual basis of the group of central units of ZG for a class of groups G properly contained in the finite strongly monomial groups. Furthermore, for another class of groups G inside the finite strongly monomial groups, we give an explicit construction of a complete set of orthogonal primitive idempotents of QG. Finally, we apply these results to describe finitely many generators of a subgroup of finite index in the group of units of ZG, this for metacyclic groups G of the form G = C-qm x C-pn with p and q different primes and the cyclic group C-pn of order p(n) acting faithfully on the cyclic group Cqm of order q(m). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free