### 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 = 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.

Original language | English |
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Pages (from-to) | 2147-2156 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 1 2009 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

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## Cite this

Pawalowski, K., & Sumi, T. (2009). The laitinen conjecture for finite solvable oliver groups.

*Proceedings of the American Mathematical Society*,*137*(6), 2147-2156. https://doi.org/10.1090/S0002-9939-09-09719-6