Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T07:36:22.755Z Has data issue: false hasContentIssue false
  • English
  • Français

Free actions of p-groups (p>3) on Sn×Sn

Published online by Cambridge University Press:  18 May 2009

Kahtan Alzubaidy
Kahtan Alzubaidy
Affiliation:
Mathematics Department, Science College, Garyounis University, Benghazi, Libya
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.

In [3] P. E. Conner showed that no abelian group with rank greater than 2 can act freely on Sn×Sn, the product of two spheres. G. Lewis [6] studied free actions of p-groups on Sn×Sn, when n is odd, n≢−l(p) and p is an odd prime. He showed that any p-group which has such an action must be abelian.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 97 - 101
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Alzubaidy, K., Metacyclic p-groups and Chern classes, Illinois J. Math. (to appear).Google Scholar
2.Burnside, W., Theory of groups of finite order, 2nd edition (reprinted Dover, 1955).Google Scholar
3.Conner, P. E., On the action of a finite group on Sn×Sn, Ann. of Math. (2) 66 (1957), 586–588.CrossRefGoogle Scholar
4.Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras (Inter-Science, 1962).Google Scholar
5.Huppert, B., Endliche Gruppen I (Springer-Verlag, 1967).CrossRefGoogle Scholar
6.Lewis, G., Free actions on Sn×Sn, Trans. Amer. Math. Soc. 132 (1968), 531–540.Google Scholar
7.Lewis, G., The integral cohomology rings of groups of order p3, Trans. Amer. Math. Soc. 132 (1968), 501–529.Google Scholar