Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Invariants of some abelian $p$-groups
in characteristic $p$


Author: Mara D. Neusel
Journal: Proc. Amer. Math. Soc. 125 (1997), 1921-1931
MSC (1991): Primary 13A50
DOI: https://doi.org/10.1090/S0002-9939-97-03814-8
MathSciNet review: 1377000
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An explicit description of the ring of polynomial invariants of cyclic groups of order $p^s$ with fixed point set of codimension 2, or with covariants of codimension 2, over a field of characteristic $p$ is given. It transpires that these rings are complete intersections. A slight generalization for some abelian $p$-groups is also derived, which leads to a result about arbitrary groups with $p$-Sylow subgroup of this type.


References [Enhancements On Off] (What's this?)

  • 1. D. Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer Verlag, New York and Berlin, 1995. CMP 95:10
  • 2. G. Ellingsrud and T. Skjelbred, Profondeur d'anneaux d'invariants en caractéristique $p$, Comp. Math. 41 (1980), 233-244. MR 82c:13015
  • 3. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th edition, Clarendon Press, Oxford, 1960.
  • 4. P. S. Landweber and R. E. Stong, The depth of rings of invariants over finite fields, Proc. New York Number Theory Seminar, 1984, Lecture Notes in Math., vol. 1240, Springer Verlag, New York, 1987. MR 88k:13004
  • 5. M. Nagata, A remark on the unique factorization theorem, J. Math. Soc. Japan 9 (1957), 143-145. MR 18:869a
  • 6. H. Nakajima, Invariants of finite abelian groups generated by transvections, Tokyo J. Math. 3 (1980), 201-214. MR 82e:14058
  • 7. L. Smith, Polynomial invariants of finite groups, A. K. Peters LTD, Wellesley, MA, 1995. CMP 95:11

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13A50

Retrieve articles in all journals with MSC (1991): 13A50


Additional Information

Mara D. Neusel
Affiliation: Institut für Algebra und Geometrie, Otto-von-Guericke-Universität, Postfach 4120, D 39016 Magdeburg, Germany
Email: mara.neusel@mathematik.uni-magdeburg.de

DOI: https://doi.org/10.1090/S0002-9939-97-03814-8
Keywords: Polynomial invariants of finite groups
Received by editor(s): October 23, 1995
Received by editor(s) in revised form: January 16, 1996
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society