Torsion units of integral group rings of metacyclic groups

Luthar, I. S. ; Bhandari, A. K. (1983) Torsion units of integral group rings of metacyclic groups Journal of Number Theory, 17 (2). pp. 270-283. ISSN 0022-314X

Full text not available from this repository.

Official URL: http://linkinghub.elsevier.com/retrieve/pii/002231...

Related URL: http://dx.doi.org/10.1016/0022-314X(83)90024-0

Abstract

Let VZ G (respectively, VQ G) denote the group of units of augmentation 1 in the integral (respectively, rational) group ring of a finite group G. It has been conjectured [[7.]] that each element of finite order of VZ G is conjugate in VQ G to an element of G (see also [1.] and [6.]). To the best of our knowledge, the only nonabelian case (other than the Hamiltonian 2-groups) where this conjecture has been verified is G = S3 [[5.], 529-534]. In this paper this conjecture is verified for the metacyclic group G = < σ , τ: σp = 1 = τq, τστ-1 = σj> (p, q primes, p = 1 mod q, jq = 1, j N= 1 mod p) by expressing VZ G and VQ G as semidirect products of groups of q × q matrices. Although S. Galovitch, I. Reiner, and S. Ullom [Mathematika. 19 (1972), 105-111] obtained a description of VZ G, the discussion of torsion units was not attempted by them.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:29973
Deposited On:23 Dec 2010 03:53
Last Modified:06 Jun 2011 10:05

Repository Staff Only: item control page