Free actions of -groups on products of lens spaces

Author:
Ergün Yalçin

Journal:
Proc. Amer. Math. Soc. **129** (2001), 887-898

MSC (2000):
Primary 57S25; Secondary 20J06, 20D15

DOI:
https://doi.org/10.1090/S0002-9939-00-05756-7

Published electronically:
September 20, 2000

MathSciNet review:
1792188

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let be an odd prime number. We prove that if acts freely on a product of equidimensional lens spaces, then . This settles a special case of a conjecture due to C. Allday. We also find further restrictions on non-abelian -groups acting freely on a product of lens spaces. For actions inducing a trivial action on homology, we reach the following characterization: A -group can act freely on a product of lens spaces with a trivial action on homology if and only if and has the -extension property. The main technique is to study group extensions associated to free actions.

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Additional Information

**Ergün Yalçin**

Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Address at time of publication:
Department of Mathematics, Bilkent University, Ankara, Turkey 06533

Email:
yalcine@math.mcmaster.ca

DOI:
https://doi.org/10.1090/S0002-9939-00-05756-7

Keywords:
Group actions,
products of lens spaces,
group extensions

Received by editor(s):
May 12, 1999

Published electronically:
September 20, 2000

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2000
American Mathematical Society