On the generalized Davenport constant and the Noether number

• Autorzy: Kálmán Cziszter , Mátyás Domokos
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Noether number; Davenport constant; Polynomial invariants

Kategorie tematyczne

• 11B75: Other combinatorial number theory
• 13A50: Actions of groups on commutative rings; invariant theory
• 13A02: Graded rings

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 9
• Strony: 1605-1615

Daty

wydano

2013-09-01

online

2013-06-28

Twórcy

autor

Kálmán Cziszter

• Central European University

autor

Mátyás Domokos

• Hungarian Academy of Sciences

Bibliografia

• [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
• [2] Cziszter K., Domokos M., Groups with large Noether bound, preprint available at http://arxiv.org/abs/1105.0679v4
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [13] Geroldinger A., Halter-Koch F., Non-Unique Factorizations, Pure Appl. Math. (Boca Raton), 278, Chapman & Hall/CRC, Boca Raton-London-New York, 2006
• [14] Halter-Koch F., A generalization of Davenport’s constant and its arithmetical applications, Colloq. Math., 1992, 63(2), 203–210
• [15] Kemper G., Separating invariants, J. Symbolic Comput., 2009, 44(9), 1212–1222 http://dx.doi.org/10.1016/j.jsc.2008.02.012
• [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
• [17] Kohls M., Kraft H., Degree bounds for separating invariants, Math. Res. Lett., 2010, 17(6), 1171–1182
• [18] Noether E., Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann., 1915, 77(1), 89–92 http://dx.doi.org/10.1007/BF01456821
• [19] Popov V.L., The constructive theory of invariants, Izv. Akad. Nauk SSSR Ser. Mat., 1981, 45(5), 1100–1120 (in Russian)
• [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
• [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
• [22] Weyl H., The Classical Groups. Their Invariants and Representations, Princeton University Press, Princeton, 1939

Identyfikatory

DOI

10.2478/s11533-013-0259-z