Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-10T21:45:11.709Z Has data issue: false hasContentIssue false
  • English
  • Français

The integral cohomology rings of some p-groups

Published online by Cambridge University Press:  24 October 2008

I. J. Leary
I. J. Leary
Affiliation:
Trinity College, Cambridge
Get access Rights & Permissions [Opens in a new window]

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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 25 - 32
Copyright
Copyright © Cambridge Philosophical Society 1991

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]AlZubaidy, K.. Rank 2 p-groups, p > 3, and Chern classes. Pacific J. Math. 103 (1982), 259–267.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), 15–64, 81–97.Google Scholar
[3]Atiyah, M. F.. Characters and the cohomology of finite groups. Inst. Hautes Études Sci. Publ. Math. 9 (1961), 23–64.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), 501–529.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 Unpublished essay (1988).Google Scholar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), 253–262.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), 1–8.Google Scholar