## Finite Presentability of S-Arithmetic Groups. Compact Presentability of Solvable GroupsThe problem of determining which S-arithmetic groups have a finite presentation is solved for arbitrary linear algebraic groups over finite extension fields of #3. For certain solvable topological groups this problem may be reduced to an analogous problem, that of compact presentability. Most of this monograph deals with this question. The necessary background material and the general framework in which the problem arises are given partly in a detailed account, partly in survey form. In the last two chapters the application to S-arithmetic groups is given: here the reader is assumed to have some background in algebraic and arithmetic group. The book will be of interest to readers working on infinite groups, topological groups, and algebraic and arithmetic groups. |

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### Contents

0 | 13 |

Filtrations of Lie algebras and groups | 27 |

A necessary condition for compact presentability | 49 |

Copyright | |

5 other sections not shown

### Other editions - View all

Finite Presentability of S-Arithmetic Groups. Compact Presentability of ... Herbert Abels Limited preview - 2006 |

Finite Presentability of S-Arithmetic Groups. Compact Presentability of ... Herbert Abels No preview available - 2014 |

### Common terms and phrases

abelian acts apply assume automorphism Banach Spaces basis called chapter claim commutator compact presentation compactly condition connected contained continuous contracting corollary corresponding defined definition denote descending central series Edited elements Equations equivalent exact sequence example extension fact field finitely presented give given hand hence holds homology homomorphism implies induces integer isomorphism K-split LEMMA Let G Lie algebra Lie group maximal module natural necessary nilpotent Lie algebra normal subgroup notations Note obtain p-adic positively independent Proceedings PROOF PROPOSITION prove Recall reductive representation resp respect result ring s-arithmetic subgroup solvable spanned subgroup of G subset sufficient Suppose surjective theorem Theory topological group unipotent unique vector space weight zero