### Abstract

For any finite group G, we impose an algebraic condition, the G ^{nil}-coset condition, and prove that any finite Oliver group G satisfying the G ^{nil}-coset condition has a smooth action on some sphere with isolated fixed points at which the tangent G-modules are not isomorphic to each other. Moreover, we prove that, for any finite non-solvable group G not isomorphic to Aut(A 6) or PΣL(2, 27), the G ^{nil}-coset condition holds if and only if rG ≥ 2, where rG is the number of real conjugacy classes of elements of G not of prime power order. As a conclusion, the Laitinen Conjecture holds for any finite non-solvable group not isomorphic to Aut(A 6).

Original language | English |
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Pages (from-to) | 303-336 |

Number of pages | 34 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 56 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 1 2013 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Pawałowski, K., & Sumi, T. (2013). The laitinen conjecture for finite non-solvable groups.

*Proceedings of the Edinburgh Mathematical Society*,*56*(1), 303-336. https://doi.org/10.1017/S0013091512000223