## Group actions and group extensions

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- Trans. Amer. Math. Soc.
**352**(2000), 2689-2700 Request permission

## Abstract:

In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if $(Z/p)^r$ acts freely on $(S^1)^k$, then $r \leq k$.## References

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## Additional Information

**Ergün Yalçin**- Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- Email: eyalcin@math.indiana.edu
- Received by editor(s): January 30, 1998
- Published electronically: February 24, 2000
- Additional Notes: Partially supported by NATO grants of the Scientific and Technical Research Council of Turkey
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**352**(2000), 2689-2700 - MSC (1991): Primary 57S25; Secondary 20J06, 20C15
- DOI: https://doi.org/10.1090/S0002-9947-00-02485-5
- MathSciNet review: 1661282