Hostname: page-component-7479d7b7d-m9pkr Total loading time: 0 Render date: 2024-07-12T13:18:07.413Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Pham Anh Minh
Affiliation:
Department of Mathematics, University of Hue. Dai hoc Tong hop Hue, Hue, Vietnam
Get access Rights & Permissions [Opens in a new window]

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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 3 , October 1996 , pp. 423 - 440
Copyright
Copyright © Cambridge Philosophical Society 1996

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]Benson, D. J. and Carlson, J. F.. The cohomology of extra-special groups. Bull. London Math. Soc. 24 (1992), 209–235.CrossRefGoogle Scholar
[2]Charlap, L. S. and Vasquez, A. T.. The cohomology of group extensions. Trans. Amer. Math. Soc. 124 (1966), 533–549.CrossRefGoogle Scholar
[3]Diethelm, T.. The mod p cohomology rings of the nonabelian split metacyclic p–groups. Arch. Math. (Basel) 44 (1985), 29–38.CrossRefGoogle Scholar
[4]Harada, M. and Kono, A.. On the integral cohomology of extraspecial 2-groups. J. PureAppl. Alg. 44 (1987), 215–219.Google Scholar
[5]Hochschild, G. and Serre, J. P.. The cohomology of group extensions. Trans. Amer. Math. Soc. 74 (1953), 110–143.CrossRefGoogle Scholar
[6]Huebschmann, J.. The mod p cohomology rings of metacyclic groups. J. Pure Appl. Alg. 60 (1989), 53–103.CrossRefGoogle Scholar
[7]Leary, I. J.. The mod p cohomology rings of some p–groups. Math. Proc. Camb. Phil. Soc. 112 (1992), 63–75.CrossRefGoogle 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]Minh, P. A. and Mui, H.. The mod p cohomology algebra of the group M(p n). Acta Math. Vietnamica 7 (1982), 17–26.Google Scholar
[10]Minh, P. A.. Modular invariant theory and cohomology algebras of extra-special p–groups. Pac. J. Math. 124 (1986), 345–363.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), 61–67.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), 139–154.CrossRefGoogle Scholar
[14]Minh, P. A.. Transfer map and Hochschild-Serre spectral sequences. J. Pure Appl. Alg., to 104 (1995), 89–95.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), 197–212.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), 449–459.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), 281–306; Contemp. Math., 158 (Amer. Math. Soc., 1994).CrossRefGoogle Scholar