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Note on the spectral sequence converging to cohomology of an extra special p-group for odd prime p

Published online by Cambridge University Press:  24 October 2008

Nobuaki Yagita
Nobuaki Yagita
Affiliation:
Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
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Extract

Extra special p-groups are groups which are central extensions of ℤ/p by elementary abelian p-groups. The cohomology ring of these groups occupies an important place in equivariant cohomology theories and in representation theories. Quillen[6] decided the cohomology for p = 2 and Tezuka-Yagita [7] studied the varieties defined by its mod p cohomology for odd prime p. However, for applications we need more information about the behaviour of the Hochschild-Serre spectral sequence (see [3] p. 295, [1] p. 6).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 35 - 41
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Allday, C.. Elementary abelian p–group actions on Lens spaces, Topology Hawaii (Doverman, K. H.). World Scientist (1992), 1–11.Google Scholar
[2]Araki, S.. Steenrod reduced power in the spectral sequences associated with fibring. Memoris Fac. Sci. Kyusu Univ. 11 (1957), 15–64.Google Scholar
[3]Benson, D. and Carlson, J.. Periodic modules with large period. Quart. J. Oxford 43 (1992), 283–296.CrossRefGoogle Scholar
[4]Hsiang, W. Y.. Cohomology theory of topological transformation groups. Ergebnisse der Math. 85 (Springer, 1975).Google Scholar
[5]Leary, I.. The integral cohomology ring of some p–groups. Math. Proc. Cambridge Phil. Soc. 110 (1991), 25–32.CrossRefGoogle Scholar
[6]Quillen, D.. The mod 2 cohomology rings of extra special 2-groups and the Spinor group. Math. Ann. 194 (1971), 197–223.CrossRefGoogle Scholar
[7]Tezuka, M. and Yagita, N.. The varieties of the mod p cohomology rings of extra special p–groups for an odd prime p. Math. Proc. Cambridge Phil. Soc. 94 (1983), 449–459.CrossRefGoogle Scholar
[8]Tezuka, M. and Yagita, N.. Calculations in mod p cohomology of extra special p–groups I. Contemporary Math. 158 (1994), 281–306.CrossRefGoogle Scholar
[9]Yagita, N.. On the dimension of spheres whose product admits a free action by a non-abelian group. Quart. J.Math. Oxford 36 (1985), 117–127.CrossRefGoogle Scholar