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Nilpotency degree of cohomology rings in characteristic 3

Author(s): Pham Anh Minh
Journal: Proc. Amer. Math. Soc. 130 (2002), 307-310.
MSC (2000): Primary 20J06; Secondary 20D15, 55R40
Posted: May 23, 2001
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Abstract: The purpose of this note is to provide a -group $\mathcal{G}$ whose mod-3 cohomology ring has a nilpotent element $\xi \in H^{*}(\mathcal{G})$ satisfying $\xi ^{3}\ne 0$ .

References:

1.: G.S. Arvunin, J.F. Carlson, Nilpotency degree of cohomology rings in characteristic two, Proc. Amer. Math. Soc. 118 (1993), 339-443. MR 93g:20098
2.: K. Inoue, A. Kono, Nilpotency of a kernel of the Quillen map, J. Math. Kyoto Univ. 33 (1993), 1047-1055. MR 95a:20053
3.: I.J. Leary, The mod- cohomology rings of some -groups, Math. Proc. Camb. Phil. Soc. 112 (1992), 63-75. MR 94a:20087
4.: R.J. Milgram, M. Tezuka, The geometry and cohomology of $M_{12}$ . II, Bol. Soc. Mat. Mexicana 1 (1995), 91-108. MR 97f:20064
5.: P.A. Minh, Essential mod- cohomology classes of -groups: an upper bound for the nilpotency degrees, Bull. London Math. Soc. 32 (2000), 285-291. MR 2001c:20106

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Additional Information:

Pham Anh Minh
Affiliation: Department of Mathematics, College of Sciences, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Address at time of publication: 53 Craig Road, Stockport SK4 2AP, England
Email: paminh@dng.vnn.vn

DOI: 10.1090/S0002-9939-01-06036-1
PII: S 0002-9939(01)06036-1
Received by editor(s): February 21, 2000
Received by editor(s) in revised form: June 12, 2000
Posted: May 23, 2001
Dedicated: To Phuong and Nin
Communicated by: Stephen D. Smith
Copyright of article: Copyright 2001, American Mathematical Society


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