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The Laitinen Conjecture for finite solvable Oliver groups


Authors: Krzysztof Pawałowski and Toshio Sumi
Journal: Proc. Amer. Math. Soc. 137 (2009), 2147-2156
MSC (2000): Primary 57S17, 57S25
Published electronically: January 26, 2009
MathSciNet review: 2480297
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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 Poznań, 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: https://doi.org/10.1090/S0002-9939-09-09719-6
Received by editor(s): May 2, 2008
Received by editor(s) in revised form: August 4, 2008
Published electronically: January 26, 2009
Communicated by: Paul Goerss
Article copyright: © Copyright 2009 American Mathematical Society