caa a22 4500 37889451X CHVBK 20180305123503.0 cr unu---uuuuu 161128e20040906xx s 000 0 eng 10.1515/jgth.2004.7.4.555 doi (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.555 Torsion-free crystallographic groups with indecomposable holonomy group. II [Elektronische Daten] [V. A. Bovdi, P. M. Gudivok, V. P. Rudko] Let K be a principal ideal domain, G a finite group, and M a KG-module which is a free K-module of finite rank on which G acts faithfully. A generalized crystallographic group is a non-split extension ℭ of M by G such that conjugation in ℭ induces the G-module structure on M. (When K = ℤ, these are just the classical crystallographic groups.) The dimension of ℭ is the K-rank of M, the holonomy group of ℭ is G, and ℭ is indecomposable if M is an indecomposable KG-module. We study indecomposable torsion-free 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 p-adic integers. We prove that the dimensions of such groups with G non-cyclic of order p 2 are unbounded. For K = ℤ, we show that there are infinitely many non-isomorphic such groups with G the alternating group of degree 4 and we study the dimensions of such groups with G cyclic of certain orders. © de Gruyter Mathematical foundations nationallicence Applied mathematics nationallicence Number theory nationallicence Bovdi V. A. aut Gudivok P. M. aut Rudko V. P. aut Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 555-569 1433-5883 7:4<555 2004 7 jgth https://doi.org/10.1515/jgth.2004.7.4.555 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/jgth.2004.7.4.555 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bovdi V. A. aut NATIONALLICENCE 700 1- Gudivok P. M. aut NATIONALLICENCE 700 1- Rudko V. P. aut NATIONALLICENCE 773 0- Journal of Group Theory Walter de Gruyter 7/4(2004-09-06), 555-569 1433-5883 7:4<555 2004 7 jgth CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter