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dc.contributor.advisorFlannery, Daneen
dc.contributor.advisorDetinko, Allaen
dc.contributor.authorRossmann, Tobiasen
dc.date.accessioned2011-09-12T12:11:45Zen
dc.date.available2011-09-12T12:11:45Zen
dc.date.issued2011-03-04en
dc.identifier.urihttp://hdl.handle.net/10379/2145en
dc.description.abstractIn 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.subjectComputational group theoryen
dc.subjectMathematicsen
dc.titleAlgorithms for Nilpotent Linear Groupsen
dc.typeThesisen
dc.contributor.funderScience Foundation Irelanden
dc.local.noteWe 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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