Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T14:34:42.456Z Has data issue: false hasContentIssue false
  • English
  • Français

The mod-p cohomology rings of some p-groups

Published online by Cambridge University Press:  24 October 2008

I. J. Leary
I. J. Leary
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS
Get access Rights & Permissions [Opens in a new window]

Extract

Throughout this paper p denotes an odd prime. The groups we shall consider are central extensions of a cyclic subgroup by Cp ⊕ Cp, and may be presented as

The group P(n) is defined for each n ≥ 3, and has order pn. The group P(3) is the non-abelian group of order p3 and exponent p. The mod-p cohomology rings of the other groups of order p3 have been known for some time (see [14] or [5] for that of the non-abelian metacyclic group), and so this paper completes the calculation of the mod-p cohomology rings of the groups of order p3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 63 - 75
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Araki, S.. Steenrod reduced powers in the spectral sequences associated with a fibering. Mem. Fac. Sci. Kyusyu Univ. Ser. A 11 (1957), 1–8.Google Scholar
[2]Benson, D. J. and Carlson, J. F.. Cohomology of extraspecial groups, submitted.Google Scholar
[3]Brown, K. S.. Cohomology of Groups (Springer-Verlag, 1982).CrossRefGoogle Scholar
[4]Burnside, W.. Theory of Finite Groups (Cambridge University Press, 1897).Google Scholar
[5]Diethelm, T.. The mod p cohomology rings of the nonabelian split metacyclic p-groups. Arch. Math. (Basel) 44 (1985), 29–38.CrossRefGoogle Scholar
[6]Huebschmann, J.. Perturbation theory and free resolutions for nilpotent groups of class 2. J. Algebra 126 (1989), 348–399.CrossRefGoogle Scholar
[7]Huebschmann, J.. Cohomology of nilpotent groups of class 2. J. Algebra 126 (1989), 400–450.CrossRefGoogle Scholar
[8]Kraines, D.. Massey Higher Products. Trans. Amer. Math. Soc. 124 (1966), 431–449.CrossRefGoogle Scholar
[9]Leary, I. J.. The cohomology of certain finite groups. Ph.D. thesis, University of Cambridge (1990).Google Scholar
[10]Leary, I. J.. The integral cohomology rings of some p-groups. Math. Proc. Cambridge Philos. Soc. 110 (1991), 25–32.CrossRefGoogle Scholar
[11]Lewis, G.. Integral cohomology rings of groups of order p3. Trans. Amer. Math. Soc. 132 (1968), 501–529.Google Scholar
[12]May, J. P.. Matric Massey products. J. Algebra 12 (1969), 533–568.CrossRefGoogle Scholar
[13]Milgram, R. J. and Tezuka, M.. The geometry and cohomology of M12 II, submitted.Google Scholar
[14]Minh, P. A. and Mui, Huynh. The mod-p cohomology algebra of the group M(pn). Acta Math. Vietnam. 7 (1982), 17–26.Google Scholar
[15]Moselle, B.. Calculations in the cohomology of finite groups. Unpublished essay (1989).Google Scholar
[16]Vasquez, R.. Nota sobre los cuadrados de Steenrod en la sucesion espectral de un espacio fibrado. Bol. Soc. Math. Mexicana 2 (1957), 1–8.Google Scholar