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Nilpotency degree of cohomology rings in characteristic two


Authors: George S. Avrunin and Jon F. Carlson
Journal: Proc. Amer. Math. Soc. 118 (1993), 339-343
MSC: Primary 20J06
DOI: https://doi.org/10.1090/S0002-9939-1993-1129871-7
MathSciNet review: 1129871
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Abstract: In this paper, we consider the cohomology ring of a finite $ 2$-group with coefficients in a field of characteristic two. We show that, for any positive integer $ n$, there exists a $ 2$-group whose cohomology ring has elements of nilpotency degree $ n + 1$ and all smaller degrees.


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

  • [1] B. Buchberger, Theoretical basis for the reduction of polynomials to canonical forms, ACM SIGSAM Bull. 39 (1976), 19-29. MR 0463136 (57:3097)
  • [2] Jon F. Carlson, Projective resolutions and degree shifting for cohomology and group rings, preprint, Proceedings of the Tsukuba Workshop on Representations of Algebras, August, 1990 (to appear). MR 1211478 (93m:20071)
  • [3] Saunders Mac Lane, Homology, Grundlehren Math. Wiss., vol. 114, Springer-Verlag, Berlin, 1963. MR 1344215 (96d:18001)
  • [4] Jean-Pierre Serre, Homologie singulière des espaces fibrés, Ann. of Math. (2) 54 (1951), 425-505. MR 0045386 (13:574g)
  • [5] -, Algèbre locale--multiplicités, Lecture Notes in Math., vol. 11, Springer-Verlag, Berlin, 1965.
  • [6] Richard P. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. (N.S.) 1 (1979), 475-511. MR 526968 (81a:20015)
  • [7] Oscar Zariski and Pierre Samuel, Commutative algebra, vol. II, Van Nostrand, New York, 1960. MR 0120249 (22:11006)

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DOI: https://doi.org/10.1090/S0002-9939-1993-1129871-7
Article copyright: © Copyright 1993 American Mathematical Society

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