# Details of talk

Title | Extending Margulis' Normal Subgroup Theorem to Commensurated Subgroups |
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Presenter | George Willis (The University of Newcastle) |

Author(s) | Prof George Willis |

Session | Algebra |

Time | 14:30:00 2016-12-08 |

Abstract | Margulis’ Normal Subgroup Theorem asserts that higher-rank arithmetic groups have few normal subgroups, for example, every normal subgroup of $SL(N,\mathbb{Z})$ is either finite or have finite index. Joint work with Yehuda Shalom extends this theorem to commensurates subgroups, that is, subgroups $N$ of $\Gamma$ such that $gNg^{-1}$ has finite index in both $N$ and $gNg^{-1}$ for every $g$ in $G$. The proof reduces to problem to Margulis’ Theorem and the talk will explain the main ideas in the reduction. |