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The mod p cohomology group of extra-special p-group of order p5 and of exponent p2

Published online by Cambridge University Press:  24 October 2008

Pham Anh Minh
Affiliation:
Department of Mathematics, University of Hue. Dai hoc Tong hop Hue, Hue, Vietnam

Extract

Let p be an odd prime number, and let M2 be the extra-special p-group of order p5 and of exponent p2. For every p-group K, we denote by H*(K) the mod p cohomology of K. The purpose of this paper is to calculate the mod p cohomology groups of M2 and of Cp2* M2 (the central product of the cyclic group Cp2 of order p2 and M2).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Benson, D. J. and Carlson, J. F.. The cohomology of extra-special groups. Bull. London Math. Soc. 24 (1992), 209235.CrossRefGoogle Scholar
[2]Charlap, L. S. and Vasquez, A. T.. The cohomology of group extensions. Trans. Amer. Math. Soc. 124 (1966), 533549.CrossRefGoogle Scholar
[3]Diethelm, T.. The mod p cohomology rings of the nonabelian split metacyclic p–groups. Arch. Math. (Basel) 44 (1985), 2938.CrossRefGoogle Scholar
[4]Harada, M. and Kono, A.. On the integral cohomology of extraspecial 2-groups. J. PureAppl. Alg. 44 (1987), 215219.Google Scholar
[5]Hochschild, G. and Serre, J. P.. The cohomology of group extensions. Trans. Amer. Math. Soc. 74 (1953), 110143.CrossRefGoogle Scholar
[6]Huebschmann, J.. The mod p cohomology rings of metacyclic groups. J. Pure Appl. Alg. 60 (1989), 53103.CrossRefGoogle Scholar
[7]Leary, I. J.. The mod p cohomology rings of some p–groups. Math. Proc. Camb. Phil. Soc. 112 (1992), 6375.CrossRefGoogle Scholar
[8]Lewis, G.. The integral cohomology rings of groups of order p 3. Trans. Amer. Math. Soc. 132 (1968), 501529.Google Scholar
[9]Minh, P. A. and Mui, H.. The mod p cohomology algebra of the group M(p n). Acta Math. Vietnamica 7 (1982), 1726.Google Scholar
[10]Minh, P. A.. Modular invariant theory and cohomology algebras of extra-special p–groups. Pac. J. Math. 124 (1986), 345363.CrossRefGoogle Scholar
[11]Minh, P. A.. On the mod p cohomology algebras of extra-special p–groups. Proc. Conf. Math. Mech. Inf., Univ. of Hanoi (1986), 6167.Google Scholar
[12]Minh, P. A.. Hochschild-Serre spectral sequences, modular invariant theory and cohomology algebras of extra-special p–groups. Thesis, Univ. of Hanoi (1990).Google Scholar
[13]Minh, P. A.. On the mod p cohomology groups of extra-special p–groups. Japan. J. Math. 18 (1992), 139154.CrossRefGoogle Scholar
[14]Minh, P. A.. Transfer map and Hochschild-Serre spectral sequences. J. Pure Appl. Alg., to 104 (1995), 8995.CrossRefGoogle Scholar
[15]Minh, P. A.. Hochschild-Serre spectral sequences of split extensions and cohomology of some extra-special p-groups. J. Pure Appl. Alg., submitted.Google Scholar
[16]Quillen, D.. The mod 2 cohomology rings of extra-special 2-groups and the spinor groups. Math. Ann. 194 (1971), 197212.CrossRefGoogle Scholar
[17]Siegel, S. F.. The spectral sequence of a split extension and the cohomology of an extraspecial group of order p 3 and of exponent p. J. Pure Appl. Alg. (to appear).Google Scholar
[18]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. Camb. Phil. Soc. 94 (1983), 449459.CrossRefGoogle Scholar
[19]Tezuka, M. and Yagita, N.. Calculations in mod p cohomology of extra-special p–groups I; in Topology and representation theory (Evanston, IL, 1992), 281306; Contemp. Math., 158 (Amer. Math. Soc., 1994).CrossRefGoogle Scholar