Torsion-free crystallographic groups with indecomposable holonomy group. II
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| 024 | 7 | 0 | |a 10.1515/jgth.2004.7.4.555 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.1515/jgth.2004.7.4.555 | ||
| 245 | 0 | 0 | |a Torsion-free crystallographic groups with indecomposable holonomy group. II |h [Elektronische Daten] |c [V. A. Bovdi, P. M. Gudivok, V. P. Rudko] |
| 520 | 3 | |a 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. | |
| 540 | |a © de Gruyter | ||
| 690 | 7 | |a Mathematical foundations |2 nationallicence | |
| 690 | 7 | |a Applied mathematics |2 nationallicence | |
| 690 | 7 | |a Number theory |2 nationallicence | |
| 700 | 1 | |a Bovdi |D V. A. |4 aut | |
| 700 | 1 | |a Gudivok |D P. M. |4 aut | |
| 700 | 1 | |a Rudko |D V. P. |4 aut | |
| 773 | 0 | |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 555-569 |x 1433-5883 |q 7:4<555 |1 2004 |2 7 |o jgth | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/jgth.2004.7.4.555 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1515/jgth.2004.7.4.555 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bovdi |D V. A. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Gudivok |D P. M. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Rudko |D V. P. |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Journal of Group Theory |d Walter de Gruyter |g 7/4(2004-09-06), 555-569 |x 1433-5883 |q 7:4<555 |1 2004 |2 7 |o jgth | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-gruyter | ||