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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On extending free group actions on spheres and a conjecture of Iwasawa


Authors: Frank Connolly and Robert Geist
Journal: Trans. Amer. Math. Soc. 274 (1982), 631-640
MSC: Primary 57S17; Secondary 57R67
MathSciNet review: 675071
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Abstract: A transfer map for Reidemeister torsion is defined and used to determine whether free actions of $ \mathbf{Z}/k$ on $ S^{2n+1}$, $ n > 1$, extend to free actions of $ \mathbf{Z}/hk$. It is shown that for $ k$ odd, every free $ \mathbf{Z}/k$ action on $ S^{2n+1}$, $ n > 1$, extends to a free $ \mathbf{Z}/2k$ action. For prime $ p$, extension of an arbitrary free $ \mathbf{Z}/p$ action to a free $ \mathbf{Z}/p^{2}$ action is reduced to a long-standing conjecture of Iwasawa.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0675071-1
PII: S 0002-9947(1982)0675071-1
Article copyright: © Copyright 1982 American Mathematical Society