### Abstract

A p-local finite group consists of a finite p-group S, together with a pairof categories which encode “conjugacy” relations among subgroups of S, and whichare modelled on the fusion in a Sylow p-subgroup of a finite group. It contains enoughinformation to define a classifying space which has many of the same properties asp-completed classifying spaces of finite groups. In this paper, we study and classifyextensions of p-local finite groups, and also compute the fundamental group of theclassifying space of a p-local finite group.

Original language | English |
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Pages (from-to) | 3791–3858 |

Number of pages | 68 |

Journal | Transactions of the American Mathematical Society |

Volume | 359 |

Issue number | 8 |

Early online date | 20 Mar 2007 |

Publication status | Published - Aug 2007 |

### Keywords

- p-local finite groups
- Extensions

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## Cite this

Broto, C., Castellana, N., Grodal, J., Levi, R., & Oliver, B. (2007). Extensions of p-local finite groups.

*Transactions of the American Mathematical Society*,*359*(8), 3791–3858.