1669

Date | Jul 16, 2014 |
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Speaker | Sejong Park |

Dept. | National University of Ireland, Galway |

Room | 129-301 |

Time | 14:00-15:00 |

Given a prime p, the p-local structure of a finite group G means the information contained in the normalizers of nontrivial p-subgroups of G. It plays an important role in the classification of finite simple groups and various local-global conjectures in modular representation theory such as Alperin's weight conjecture. The notion of the p-local structure of a finite group G was formalized by Llius Puig in the early 1990s as a certain category of p-groups, called a fusion system. Since then it has been studied extensively, and now it is viewed as the right setup to study p-local structures. One important feature of fusion systems is that they are not exactly the same as finite groups, but at the same time they are quite close to finite groups, whence giving flexibility together with technical difficulty. In this introductory talk, we will give motivation for studying fusion systems, define them and discuss various realizations of fusion systems via infinite groups, finite groups, bisets and partial groups.

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