Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T06:20:28.688Z Has data issue: false hasContentIssue false
  • English
  • Français

On the K-theory of the quaternion group

Published online by Cambridge University Press:  26 February 2010

M. E. Keating
M. E. Keating
Affiliation:
Imperial College, London, S.W.7.
Get access

Extract

The main purpose of this paper is to evaluate the Whitehead group K1 (Zπ) of the quaternion group π of order 8. We show that the natural mapping of the units ± π of Zπ into K1(Zπ) induces an isomorphism between K1(Zπ) and ± V, where V, Klein's 4-group, is the commutator quotient group of π.

Type
Research Article
Information
Mathematika , Volume 20 , Issue 1 , June 1973 , pp. 59 - 62
Copyright
Copyright © University College London 1973

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

1. Bass, H., Algebraic K-theory (Benjamin, New York, 1968).Google Scholar
2. Galovich, S., Reiner, I. and Ullom, S., “Class groups for integral representations of metacyclic groups”, Mathematika, 19 (1972), 105–111.CrossRefGoogle Scholar
3. Higman, G., “The units of group rings”, Proc. Land. Math. Soc, 107 (1940), 231–248.CrossRefGoogle Scholar
4. Lee, R. and Thomas, C. B., “Free actions by finite groups on S3”, Bull. Amer. Math. Soc. (to appear).Google Scholar
5. Martinet, J., “Modules sur l'algèbre du groupe quaternionien” Ann. Sci. de l'École Norm. Sup., 4e serie t.4 fasc.3 1971.CrossRefGoogle Scholar
6. Reiner, I. and Ullom, S., “A Mayer-Vietoris sequence for class groups”, J. Algebra (to appear).Google Scholar
7. Serre, J. P., “Modules projectifes et espaces fibrés à fibre vectorielle”, Séminaire Dubreuil, exposé 23, 1968, p. 23–01 a 23–18.Google Scholar