## Uniform Boundedness of Groups

dc.contributor.advisor | Professor Benjamin Martin | |

dc.contributor.author | FAWAZ IBRAHIM ASEERI | |

dc.date | 2022 | |

dc.date.accessioned | 2022-06-04T19:35:06Z | |

dc.date.available | 2022-05-31 09:52:57 | |

dc.date.available | 2022-06-04T19:35:06Z | |

dc.description.abstract | Let G be a group. Then G is said to be bounded provided that every conjugation-invariant norm on G has a finite diameter. We say that G is uniformly bounded if the supremum of the diameters of G with respect to all its finite normally generating subsets, denoted by Delta(G), is finite. This concept is a strengthening of boundedness and was introduced by Kedra,Libman and Martin in 2021 .They showed that every finitely normally generated linear algebraic group H over an algebraically closed field is uniformly bounded and ,Delta(H) < 4dim(H)+Delta (H/H^{0}) (01) .where H^{0} is the identity component of H Let n > 1 be a natural number. Let H:=SL_2(C) or PSL_2(C). We find the exact values of Delta(H^n), thus improving (01) in these particular cases. We also introduce a new method, based on the so-called rational canonical form, to estimate Delta(SL_3(C)) and Delta(SL_3(R)). We find that 3 < Delta(SL_3(C)) < 5, while (01) only shows that Delta(SL_3(C))< 32. We also determine the exact value of Delta(G), where G is a finite dihedral group | |

dc.format.extent | 146 | |

dc.identifier.other | 111176 | |

dc.identifier.uri | https://drepo.sdl.edu.sa/handle/20.500.14154/66430 | |

dc.language.iso | en | |

dc.publisher | Saudi Digital Library | |

dc.title | Uniform Boundedness of Groups | |

dc.type | Thesis | |

sdl.degree.department | Mathematics | |

sdl.degree.grantor | University of Aberdeen | |

sdl.thesis.level | Doctoral | |

sdl.thesis.source | SACM - United Kingdom |