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Proceedings of the American Mathematical Society

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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
MathSciNet review: 1377000
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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. Geir Ellingsrud and Tor Skjelbred, Profondeur d’anneaux d’invariants en caractéristique 𝑝, Compositio Math. 41 (1980), no. 2, 233–244 (French). MR 581583
  • 3. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th edition, Clarendon Press, Oxford, 1960.
  • 4. Peter S. Landweber and Robert E. Stong, The depth of rings of invariants over finite fields, Number theory (New York, 1984–1985) Lecture Notes in Math., vol. 1240, Springer, Berlin, 1987, pp. 259–274. MR 894515,
  • 5. M. Nagata, A remark on the unique factorization theorem, J. Math. Soc. Japan 9 (1957), 143-145. MR 18:869a
  • 6. Haruhisa Nakajima, Invariants of finite abelian groups generated by transvections, Tokyo J. Math. 3 (1980), no. 2, 201–214. MR 605089,
  • 7. L. Smith, Polynomial invariants of finite groups, A. K. Peters LTD, Wellesley, MA, 1995. CMP 95:11

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Additional Information

Mara D. Neusel
Affiliation: Institut für Algebra und Geometrie, Otto-von-Guericke-Universität, Postfach 4120, D 39016 Magdeburg, Germany

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