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The Laitinen Conjecture for finite non-solvable groups
Published online by Cambridge University Press: 05 December 2012
Abstract
For any finite group G, we impose an algebraic condition, the Gnil-coset condition, and prove that any finite Oliver group G satisfying the Gnil-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(A6) or PΣL(2, 27), the Gnil-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(A6).
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 303 - 336
- Copyright
- Copyright © Edinburgh Mathematical Society 2012
References
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