Lower degree bounds for modular vector invariants

Author:
Ugur Madran

Journal:
Proc. Amer. Math. Soc. **135** (2007), 987-995

MSC (2000):
Primary 13A50

DOI:
https://doi.org/10.1090/S0002-9939-06-08574-1

Published electronically:
October 11, 2006

MathSciNet review:
2262898

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite group of order divisible by a prime acting on an vector space where is the field with elements and . Consider the diagonal action of on copies of This note sharpens a lower bound for for groups which have an element of order whose Jordan blocks have sizes at most 2.

**[B]**D. J. Benson,*Polynomial invariants of finite groups*, Cambridge Univ. Press, Cambridge, 1993. MR**1249931 (94j:13003)****[CH]**H. E. A. Campbell and I. P. Hughes, Vector invariants of : a proof of a conjecture of Richman.*Adv. Math.***126**(1997), no. 1, 1-20. MR**1440251 (98c:13007)****[CLO]**D. Cox, J. Little and D. O'Shea,*Ideals, varieties, and algorithms*, Springer, New York, 1992. MR**1189133 (93j:13031)****[K]**G. Kemper, Lower degree bounds for modular invariants and a question of I. Hughes.*Transform. Groups***3**(1998), no. 2, 135-144. MR**1628445 (99f:13004)****[M]**U. Madran, Modular Vector Invariants.*Ph.D. Dissertation*, Bilkent Univ., Ankara, to appear.*will be available online through Bilkent University Library Thesis Database.***[N1]**E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen.*Math. Ann.***77**(1916), 89-92. MR**1511848****[N2]**E. Noether, Der Endlichkeitssatz der Invarianten endlicher linear Gruppen der Charakteristik .*Nachr. Akad. Wiss. Göttingen*(1926), 28-35.**[R1]**D. R. Richman, On vector invariants over finite fields.*Adv. Math.***81**(1990), no. 1, 30-65. MR**1051222 (91g:15020)****[R2]**D. R. Richman, Invariants of finite groups over fields of characteristic .*Adv. Math.***124**(1996), no. 1, 25-48. MR**1423197 (97i:13005)****[S1]**L. Smith, Polynomial invariants of finite groups, A survey of recent developments.*Bull. Amer. Math. Soc. (N.S.)***34**(1997), no. 3, 211-250. MR**1433171 (98i:13009)****[S2]**L. Smith,*Polynomial invariants of finite groups*, A K Peters, Wellesley, MA, 1995. MR**1328644 (96f:13008)****[Ste]**S. A. Stepanov, Vector invariants of symmetric groups in the case of a field of prime characteristic. Translation in*Discrete Math. Appl.***10**(2000), no. 5, 455-468. MR**1826176 (2002e:13014)****[Stu]**B. Sturmfels,*Algorithms in invariant theory*, Springer, Vienna, 1993. MR**1255980 (94m:13004)**

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Additional Information

**Ugur Madran**

Affiliation:
Department of Mathematics, Bilkent University, Bilkent, 06800 Ankara, Turkey

Email:
madran@fen.bilkent.edu.tr, madran@member.ams.org

DOI:
https://doi.org/10.1090/S0002-9939-06-08574-1

Keywords:
Modular invariant theory,
vector invariants,
degree bound

Received by editor(s):
September 9, 2005

Received by editor(s) in revised form:
November 11, 2005

Published electronically:
October 11, 2006

Additional Notes:
The author was supported in part by TÜBİTAK

Communicated by:
Bernd Ulrich

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.