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Algorithms for Nilpotent Linear Groups

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dc.contributor.advisor Flannery, Dane en
dc.contributor.advisor Detinko, Alla en
dc.contributor.author Rossmann, Tobias en
dc.date.accessioned 2011-09-12T12:11:45Z en
dc.date.available 2011-09-12T12:11:45Z en
dc.date.issued 2011-03-04 en
dc.identifier.uri http://hdl.handle.net/10379/2145 en
dc.description.abstract In this thesis, we develop practical algorithms for irreducibility and primitivity testing of finite nilpotent linear groups defined over various fields of characteristic zero, including number fields and rational function fields over number fields. For a reducible group, we can construct a proper submodule. For an irreducible but imprimitive group, we exhibit a system of imprimitivity. An implementation of the above-mentioned algorithms is publicly available as a stand-alone package and also included in recent versions of the Magma computer algebra system. In addition to the above, we also develop an algorithm for deciding irreducibility of possibly infinite nilpotent linear groups defined over number fields. Finally, we study the structure of primitive finite nilpotent linear groups over number fields. en
dc.subject Computational group theory en
dc.subject Mathematics en
dc.title Algorithms for Nilpotent Linear Groups en
dc.type Thesis en
dc.contributor.funder Science Foundation Ireland en
dc.local.note We develop algorithms for irreducibility and primitivity testing of finite nilpotent linear groups over fields of characteristic zero. An implementation is publicly available. We also develop an algorithm for deciding irreducibility of infinite nilpotent linear groups over number fields. Finally, we study primitive finite nilpotent linear groups over number fields. en

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