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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

The Laitinen Conjecture for finite solvable Oliver groups

Author(s): Krzysztof Pawałowski; Toshio Sumi
Journal: Proc. Amer. Math. Soc. 137 (2009), 2147-2156.
MSC (2000): Primary 57S17, 57S25
Posted: January 26, 2009
MathSciNet review: 2480297
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Abstract | References | Similar articles | Additional information

Abstract: For smooth actions of $ G$ on spheres with exactly two fixed points, the Laitinen Conjecture proposed an answer to the Smith question about the $ G$-modules determined on the tangent spaces at the two fixed points. Morimoto obtained the first counterexample to the Laitinen Conjecture for $ G = {\rm Aut}(A_6)$. By answering the Smith question for some finite solvable Oliver groups $ G$, we obtain new counterexamples to the Laitinen Conjecture, presented for the first time in the case where $ G$ is solvable.

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Additional Information:

Krzysztof Pawałowski
Affiliation: Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul. Umultowska 87, 61-614 Poznan, Poland
Email: kpa@amu.edu.pl

Toshio Sumi
Affiliation: Department of Art and Information Design, Faculty of Design, Kyushu University, 4-9-1 Shiobaru, Minami-ku, Fukuoka, 815-8540, Japan
Email: sumi@design.kyushu-u.ac.jp

DOI: 10.1090/S0002-9939-09-09719-6
PII: S 0002-9939(09)09719-6
Received by editor(s): May 2, 2008,
Received by editor(s) in revised form: August 4, 2008
Posted: January 26, 2009
Communicated by: Paul Goerss
Copyright of article: Copyright 2009, American Mathematical Society




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