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Polenta

Polycyclic presentations for matrix groups

1.3.10

29 March 2022

Björn Assmann

Copyright

© 2003-2007 by Björn Assmann

The Polenta package is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

Acknowledgements

We appreciate very much all past and future comments, suggestions and contributions to this package and its documentation provided by GAP users and developers.

Contents

1.1 The package

1.2 Polycyclic groups

2 Methods for matrix groups

2.1 Polycyclic presentations of matrix groups

  2.1-1 PcpGroupByMatGroup
  2.1-2 IsomorphismPcpGroup
  2.1-3 ImagesRepresentative
  2.1-4 IsSolvableGroup
  2.1-5 IsTriangularizableMatGroup
  2.1-6 IsPolycyclicGroup

2.2 Module series

  2.2-1 RadicalSeriesSolvableMatGroup
  2.2-2 HomogeneousSeriesAbelianMatGroup
  2.2-3 HomogeneousSeriesTriangularizableMatGroup
  2.2-4 CompositionSeriesAbelianMatGroup
  2.2-5 CompositionSeriesTriangularizableMatGroup

2.3-1 SubgroupsUnipotentByAbelianByFinite

2.4-1 PolExamples

3 An example application

3.1 Presentation for rational matrix groups

3.2 Modules series

3.3 Triangularizable subgroups

4.1 Installing this package

4.2 Loading the Polenta package

4.3 Running the test suite

5 Information Messages

5.1-1 InfoPolenta

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