Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-04-30T19:48:57.167Z Has data issue: false hasContentIssue false
  • English
  • Français

Whitehead groups of semidirect products of free groups

Published online by Cambridge University Press:  18 May 2009

Koo-Guan Choo
Koo-Guan Choo
Affiliation:
Department Of Pure Mathematics, University Of Sydney, Sydney, N.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let G be a group. We denote the Whitehead group of G by Wh G and the projective class group of the integral group ring ℤ(G) of G by . Let α be an automorphism of G and T an infinite cyclic group. Then we denote by G ×αT the semidirect product of G and T with respect to α. For undefined terminologies used in the paper, we refer to [3] and [7].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 19 , Issue 2 , July 1978 , pp. 155 - 158
Copyright
Copyright © Glasgow Mathematical Journal Trust 1978

References

REFERENCES

1.Bass, H., Heller, A. and Swan, R. G., The Whitehead group of a polynomial extension, Inst. Hautes Études Sri. Publ. Math. No. 22 (1964), 61–79. MR30 #4806.Google Scholar
2.Choo, K. G., Lam, K. Y. and Luft, E., On free product of rings and the coherence property, Algebraic K-theory II: “Classical” algebraic K-theory and connections with arithmetic, Lecture Notes in Mathematics 342 (Springer, 1973), 135–143. MR 50 #13154.Google Scholar
3.Choo, K. G., The projective class group of the fundamental group of a surface is trivial, Proc. Amer. Math. Soc. 40 (1973), 42–46. MR48 #2222.CrossRefGoogle Scholar
4.Choo, K. G., Whitehead groups of certain semidirect products of free groups, Proc. Amer. Math. Soc. 43 (1974), 2630. MR49 #2890.CrossRefGoogle Scholar
5.Choo, K. G., Whitehead groups of certain semidirect products of free groups, II, Nanta Math. 9 (1976), 138–140.Google Scholar
6.Choo, K. G., The projective class groups of certain semidirect products of free groups, Nanta Math. 10 (1977), 44–46.Google Scholar
7.Farrell, F. T. and Hsiang, W. C., A formula for K1Rα[T], Proc. Sympos. Pure Math., vol. 17, (Amer. Math. Soc, 1970), 192–218. MR41 #5457.Google Scholar
8.Farrell, F. T., The obstruction of fibering a manifold over a circle, Indiana Univ. Math. J. 21 (1971), 315–346.Google Scholar
9.Gersten, S. M., K-theory of free rings, Comm. Algebra 1 (1974), 39–64.CrossRefGoogle Scholar
10.Stallings, J., Whitehead torsion of free products, Ann. of Math. 82 (1965), 354–363. MR31 #3518.Google Scholar