Nilpotency degree of cohomology rings in characteristic 𝑝

Minh, Pham

doi:10.1090/S0002-9939-02-06550-4

Nilpotency degree of cohomology rings in characteristic $p$
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by Pham Anh Minh

Proc. Amer. Math. Soc. 131 (2003), 363-368

DOI: https://doi.org/10.1090/S0002-9939-02-06550-4

Published electronically: June 3, 2002

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Abstract:

Let $p$ be an odd prime number. The purpose of this paper is to provide a $p$-group $\mathcal {G}$ whose mod-$p$ cohomology ring has a nilpotent element $\xi \in H^{*}(\mathcal {G})$ satisfying $\xi ^{p}\ne 0$.

References

George S. Avrunin and Jon F. Carlson, Nilpotency degree of cohomology rings in characteristic two, Proc. Amer. Math. Soc. 118 (1993), no. 2, 339–343. MR 1129871, DOI 10.1090/S0002-9939-1993-1129871-7
N. Blackburn, On a special class of $p$-groups, Acta Math. 100 (1958), 45–92. MR 102558, DOI 10.1007/BF02559602
Leonard Evens, Terminal $p$-groups, Illinois J. Math. 12 (1968), 682–699. MR 241535
Koichi Inoue and Akira Kono, Nilpotency of a kernel of the Quillen map, J. Math. Kyoto Univ. 33 (1993), no. 4, 1047–1055. MR 1251214, DOI 10.1215/kjm/1250519128
P. A. Minh, On the mod p cohomology groups of extra-special p-groups, Japan. J. Math. 18 (1992), 139-154.
Pham Anh Minh, Essential mod-$p$ cohomology classes of $p$-groups: an upper bound for nilpotency degrees, Bull. London Math. Soc. 32 (2000), no. 3, 285–291. MR 1750170, DOI 10.1112/S0024609399006785
Pham Anh Minh, Evens norm and restriction maps in mod-$p$ cohomology of $p$-groups, Math. Proc. Cambridge Philos. Soc. 129 (2000), no. 2, 253–262. MR 1765913, DOI 10.1017/S0305004100004564
—, Nilpotency degree of cohomology rings in characteristic 3, Proc. Amer. Math. Soc. 130 (2002), 307-310.
Daniel Quillen, The Adams conjecture, Topology 10 (1971), 67–80. MR 279804, DOI 10.1016/0040-9383(71)90018-8