Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T00:57:51.919Z Has data issue: false hasContentIssue false

Stable splittings of classifying spaces of metacyclic 2-groups

Published online by Cambridge University Press:  24 October 2008

Jill Dietz
Affiliation:
Department of Mathematics, GN-50, University of Washington, Seattle, WA 98195, USA

Abstract

We determine the stable decompositions of the classifying spaces of metacyclic 2-groups into wedges of indecomposable spectra. The stable decompositions of classifying spaces of finite groups with metacyclic 2-Sylow subgroups are also determined.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1994

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]Burnside, W.. Theory of Groups of Finite Order (Cambridge University Press, 1897).Google Scholar
[2]Dietz, J.. Stable splittings of classifying spaces of metacyclic p-groups, p odd (to appear). J. Pure and Applied Algebra.Google Scholar
[3]Harris, J. and Kuhn, N.. Stable decompositions of classifying spaces of finite abelian p-groups. Math. Proc. Cambridge Phil. Soc. 103 (1988), 427449.CrossRefGoogle Scholar
[4]Huebschmann, J.. The mod-p cohomology rings of metacyclic groups. J. Pure and Applied Algebra 60 (1989), 53103.CrossRefGoogle Scholar
[5]Martino, J.. Stable splittings and the Sylow 2-subgroups of SL 3(Fq), q odd. (Ph.D. Dissertation, Northwester Univ., 1988).Google Scholar
[6]Martino, J. and Priddy, S.. Classification of BG for groups with dihedral or quaternion Sylow 2-subgroups. J. Pure and Applied Algebra 73 (1991), 1321.CrossRefGoogle Scholar
[7]Martino, J. and Priddy, S.. The complete stable splitting for the classifying space of a finite group. Topology 31(1992), 143156.CrossRefGoogle Scholar
[8]Mitchell, S. and Priddy, S.. Stable splittings derived from the Steinberg module. Topology 22 (1983), 285298.CrossRefGoogle Scholar
[9]Mitchell, S. and Priddy, S.. Symmetric product spectra and splittings of classifying spaces. Amer. J. Math. 106 (1984), 219232.CrossRefGoogle Scholar
[10]Nishida, G.. Stable homotopy type of classifying spaces of finite groups. Algebraic and Topological Theories (1985), 391404.Google Scholar
[11]Priddy, S.. On characterizing summands in the classifying space of a group. I. Amer. J. Math. 112 (1990), 737748.CrossRefGoogle Scholar
[12]Priddy, S.. On Characterizing Summands in the Classifying Space of a Group. II. Homotopy theory and related topics. Lecture Notes in Math., 1418. (Springer, 1990).Google Scholar
[13]Thomas, A. D. and Wood, G. V.. Group Tables. Shiva Math. Series 2 (Shiva Publications, 1980).Google Scholar