Bódi, Viktor and Gudivok, P. M. and Rudko, V. P. (2004) Torsionfree crystallographic groups with indecomposable holonomy group II. Journal of Group Theory, 7 (4). pp. 555569. ISSN 14335883 (print), 14354446 (online)

PDF
1037232.pdf Download (299Kb) 
Abstract
Let K be a principal ideal domain, G a finite group, and M a KGmodule which is a free Kmodule of finite rank on which G acts faithfully. A generalized crystallographic group is a nonsplit extension C of M by G such that conjugation in C induces the Gmodule structure on M. ( When K = Z, these are just the classical crystallographic groups.) The dimension of C is the Krank of M, the holonomy group of C is G, and C is indecomposable if M is an indecomposable KGmodule. We study indecomposable torsionfree generalized crystallographic groups with holonomy group G when K is Z, or its localization Z((p)) at the prime p, or the ring Z(p) of padic integers. We prove that the dimensions of such groups with G noncyclic of order p(2) are unbounded. For K = Z, we show that there are infinitely many nonisomorphic such groups with G the alternating group of degree 4 and we study the dimensions of such groups with G cyclic of certain orders.
Item Type:  Article 

Subjects:  Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra 
Depositing User:  Erika Bilicsi 
Date Deposited:  19 Nov 2012 09:02 
Last Modified:  19 Nov 2012 09:02 
URI:  http://real.mtak.hu/id/eprint/3395 
Actions (login required)
View Item 