On the generalized Davenport constant and the Noether number
Kálmán Cziszter; Mátyás Domokos
Open Mathematics (2013)
- Volume: 11, Issue: 9, page 1605-1615
- ISSN: 2391-5455
Access Full Article
topAbstract
topHow to cite
topKálmán Cziszter, and Mátyás Domokos. "On the generalized Davenport constant and the Noether number." Open Mathematics 11.9 (2013): 1605-1615. <http://eudml.org/doc/269716>.
@article{KálmánCziszter2013,
abstract = {Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.},
author = {Kálmán Cziszter, Mátyás Domokos},
journal = {Open Mathematics},
keywords = {Noether number; Davenport constant; Polynomial invariants; polynomial invariants},
language = {eng},
number = {9},
pages = {1605-1615},
title = {On the generalized Davenport constant and the Noether number},
url = {http://eudml.org/doc/269716},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Kálmán Cziszter
AU - Mátyás Domokos
TI - On the generalized Davenport constant and the Noether number
JO - Open Mathematics
PY - 2013
VL - 11
IS - 9
SP - 1605
EP - 1615
AB - Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.
LA - eng
KW - Noether number; Davenport constant; Polynomial invariants; polynomial invariants
UR - http://eudml.org/doc/269716
ER -
References
top- [1] Benson D.J., Polynomial Invariants of Finite Groups, London Math. Soc. Lecture Note Ser., 190, Cambridge University Press, Cambridge, 1993 http://dx.doi.org/10.1017/CBO9780511565809 Zbl0864.13001
- [2] Cziszter K., Domokos M., Groups with large Noether bound, preprint available at http://arxiv.org/abs/1105.0679v4 Zbl1314.13012
- [3] Cziszter K., Domokos M., Noether’s bound for the groups with a cyclic subgroup of index two, preprint available at http://arxiv.org/abs/1205.3011v1 Zbl1307.13009
- [4] Delorme Ch., Ordaz O., Quiroz D., Some remarks on Davenport constant, Discrete Math., 2001, 237(1–3), 119–128 http://dx.doi.org/10.1016/S0012-365X(00)00365-4 Zbl1003.20025
- [5] Derksen H., Polynomial bounds for rings of invariants, Proc. Amer. Math. Soc., 2001, 129(4), 955–963 http://dx.doi.org/10.1090/S0002-9939-00-05698-7 Zbl0969.13003
- [6] Derksen H., Kemper G., Computational Invariant Theory, Invariant Theory Algebr. Transform. Groups, I, Encyclopaedia Math. Sci., 130, Springer, Berlin, 2002 http://dx.doi.org/10.1007/978-3-662-04958-7
- [7] Domokos M., Hegedűs P., Noether’s bound for polynomial invariants of finite groups, Arch. Math. (Basel), 2000, 74(3), 161–167 http://dx.doi.org/10.1007/s000130050426 Zbl0967.13004
- [8] Fleischmann P., The Noether bound in invariant theory of finite groups, Adv. Math., 2000, 156(1), 23–32 http://dx.doi.org/10.1006/aima.2000.1952 Zbl0973.13003
- [9] Fleischmann P., On invariant theory of finite groups, In: Invariant Theory in All Characteristics, CRM Proc. Lecture Notes, 35, American Mathematical Society, Providence, 2004, 43–69 Zbl1083.13002
- [10] Fogarty J., On Noether’s bound for polynomial invariants of a finite group, Electron. Res. Announc. Amer. Math. Soc., 2001, 7, 5–7 http://dx.doi.org/10.1090/S1079-6762-01-00088-9 Zbl0980.13003
- [11] Freeze M., Schmid W.A., Remarks on a generalization of the Davenport constant, Discrete Math., 2010, 310(23), 3373–3389 http://dx.doi.org/10.1016/j.disc.2010.07.028 Zbl1228.05302
- [12] Gao W., Geroldinger A., Zero-sum problems in finite abelian groups: a survey, Expo. Math., 2006, 24(4), 337–369 http://dx.doi.org/10.1016/j.exmath.2006.07.002 Zbl1122.11013
- [13] Geroldinger A., Halter-Koch F., Non-Unique Factorizations, Pure Appl. Math. (Boca Raton), 278, Chapman & Hall/CRC, Boca Raton-London-New York, 2006 Zbl1117.13004
- [14] Halter-Koch F., A generalization of Davenport’s constant and its arithmetical applications, Colloq. Math., 1992, 63(2), 203–210 Zbl0760.11031
- [15] Kemper G., Separating invariants, J. Symbolic Comput., 2009, 44(9), 1212–1222 http://dx.doi.org/10.1016/j.jsc.2008.02.012 Zbl1172.13001
- [16] Knop F., On Noether’s and Weyl’s bound in positive characteristic, In: Invariant Theory in All Characteristics, CRM Proc. Lecture Notes, 35, American Mathematical Society, Providence, 2004, 175–188 Zbl1070.13007
- [17] Kohls M., Kraft H., Degree bounds for separating invariants, Math. Res. Lett., 2010, 17(6), 1171–1182 Zbl1230.13010
- [18] Noether E., Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 1915, 77(1), 89–92 http://dx.doi.org/10.1007/BF01456821 Zbl45.0198.01
- [19] Popov V.L., The constructive theory of invariants, Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45(5), 1100–1120 (in Russian) Zbl0478.14006
- [20] Schmid B.J., Finite groups and invariant theory, In: Topics in Invariant Theory, Paris, 1989/1990, Lect. Notes in Math., 1478, Springer, Berlin, 1991, 35–66 http://dx.doi.org/10.1007/BFb0083501 Zbl0770.20004
- [21] Sezer M., Sharpening the generalized Noether bound in the invariant theory of finite groups, J. Algebra, 2002, 254(2), 252–263 http://dx.doi.org/10.1016/S0021-8693(02)00018-2 Zbl1058.13005
- [22] Weyl H., The Classical Groups. Their Invariants and Representations, Princeton University Press, Princeton, 1939
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.