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Niemeyer Groups and Geometry Slides 2004

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Niemeyer, Groups and Geometry slides
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  Groups and GeometryAlice NiemeyerGroupsFactor GroupsClassical GroupsProjective SpacesPolar SpacesSymplectic GroupsGeneralised QuadranglesAcknowledgements Groups and Geometry Alice Niemeyer The University of Western Australia September 2004  Groups and GeometryAlice NiemeyerGroupsFactor GroupsClassical GroupsProjective SpacesPolar SpacesSymplectic GroupsGeneralised QuadranglesAcknowledgements Simple Groups In Chemistry compounds are made up of elements.Is there an analouge for finite groups?YES! Simple groups are the building blocks.  Groups and GeometryAlice NiemeyerGroupsFactor GroupsClassical GroupsProjective SpacesPolar SpacesSymplectic GroupsGeneralised QuadranglesAcknowledgements Normal Subgroups A subgroup  N   of a group  G   is called  normal  if   g  − 1 ng   ∈  N   for all  g   ∈  G   and  n  ∈  N  .A group is called  simple   if its only normalsubgroups are the group itself and the trivialsubgroup.  Groups and GeometryAlice NiemeyerGroupsFactor GroupsClassical GroupsProjective SpacesPolar SpacesSymplectic GroupsGeneralised QuadranglesAcknowledgements Factor Groups The cosets of a normal subgroup  N   in  G   forma group, called the factor group  G  / N   of   G  over  N  .
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