### Abstract

Let G be a finite group. The Smith equivalence for real G-modules of finite dimension gives a subset of real representation ring, called the primary Smith set. Since the primary Smith set is not additively closed in general, it is an interesting problem to find a subset which is additively closed in the real representation ring and occupies a large portion of the primary Smith set. In this paper we introduce an additively closed subset of the primary Smith set by means of smooth one-fixed-point G-actions on spheres, and we give evidences that the subset occupies a large portion of the primary Smith set if G is an Oliver group.

Original language | English |
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Pages (from-to) | 1003-1013 |

Number of pages | 11 |

Journal | Osaka Journal of Mathematics |

Volume | 53 |

Issue number | 4 |

Publication status | Published - Oct 1 2016 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Morimoto, M. (2016). One-fixed-point actions on spheres and smith sets.

*Osaka Journal of Mathematics*,*53*(4), 1003-1013.