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The integral cohomology rings of some p-groups

Published online by Cambridge University Press:  24 October 2008

I. J. Leary
Affiliation:
Trinity College, Cambridge

Extract

We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested independently by P. H. Kropholler and J. Huebschmann. This construction has also been used by the author to calculate the mod-p cohomology of the same groups and by B. Moselle to obtain partial results concerning the mod-p cohomology of the extra special p-groups [7], [9].

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]AlZubaidy, K.. Rank 2 p-groups, p > 3, and Chern classes. Pacific J. Math. 103 (1982), 259267.CrossRefGoogle Scholar
[2]Araki, S.. Steenrod reduced powers in the spectral sequences associated with a fibering I, II. Mem. Fac. Sci. Kyusyu Univ. Series (A) Math. 11 (1957), 1564, 8197.Google Scholar
[3]Atiyah, M. F.. Characters and the cohomology of finite groups. Inst. Hautes Études Sci. Publ. Math. 9 (1961), 2364.CrossRefGoogle Scholar
[4]Brown, K. S.. Gohomology of Groups (Springer-Verlag, 1982).CrossRefGoogle Scholar
[5]Huebschmann, J.. Perturbation theory and free resolutions for nilpotent groups of class 2. J. Algebra (to appear).Google Scholar
[6]Huebschmann, J.. Cohomology of nilpotent groups of class 2. J. Algebra (to appear).Google Scholar
[7]Leary, I. J.. The mod-p cohomology rings of some p-groups (in preparation).Google Scholar
[8]Lewis, G.. The integral cohomology rings of groups of order p 3. Trans. Amer. Math. Soc. 132 (1968), 501529.Google Scholar
[9]Moselle, B.. Calculations in the cohomology of finite groups. Unpublished essay (1988).Google Scholar
[10]Thomas, C. B.. Riemann–Roch formulae for group representations. Mathematika 20 (1973), 253262.CrossRefGoogle Scholar
[11]Thomas, C. B.. Characteristic Classes and the Cohomology of Finite Groups(Cambridge University Press, 1986).Google Scholar
[12]Vasquez, R.. Nota sobre los cuadrados de Steenrod en Ia sucesion espectral de un espacio fibrado. Bol. Soc. Mat. Mexicana 2 (1957), 18.Google Scholar