A new family of finite Oliver groups satisfying the Laitinen Conjecture

摘要

This paper is concerned with the Laitinen Conjecture. The conjecture predicts an answer to the Smith question [22] which reads as follows. Is it true that for a finite group G acting smoothly on a sphere with exactly two fixed points, the tangent spaces at the fixed points have always isomorphic RG-module structures defined by differentiation of the action? Using the technique of induction of group representations, we indicate a new (for the first time, infinite) family of finite Oliver groups for which the Laitinen Conjecture holds. (C) 2020 Elsevier B.V. All rights reserved.