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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Free actions of finite groups on products
of symmetric powers of even spheres


Authors: Satya Deo and Jitendra Kumar Maitra
Journal: Proc. Amer. Math. Soc. 128 (2000), 299-306
MSC (1991): Primary 57S17; Secondary 57S05
Published electronically: June 21, 1999
MathSciNet review: 1646310
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Abstract: This paper answers a question on the existence of free actions on products of symmetric powers of even-spheres. The main objective is to show that a finite group $G$ acts freely on a finite product of symmetric powers of even-dimensional spheres iff it can act freely on a suitable product of even-dimensional spheres themselves.


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Additional Information

Satya Deo
Affiliation: Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India
Email: sdt@rdunijb.ren.nic.in

Jitendra Kumar Maitra
Affiliation: Department of Mathematics and Computer Science, R.D. University, Jabalpur - 482 001, India
Email: maitra@rdunijb.ren.nic.in

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05193-X
PII: S 0002-9939(99)05193-X
Keywords: Lefschetz number, free action, symmetric powers, Wreath products
Received by editor(s): July 29, 1997
Received by editor(s) in revised form: March 24, 1998
Published electronically: June 21, 1999
Additional Notes: While carrying out this work, the first author was supported by the UGC research grant no. F 8-5/94(SR-I) and the second author was supported by Dr. K.S. Krishnan Research Fellowship, awarded by the Department of Atomic Energy (No. 11/18/93-G), Govt. of India.
Communicated by: Ralph Cohen
Article copyright: © Copyright 1999 American Mathematical Society