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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 Introduction
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 Subgroups
2.3-1 SubgroupsUnipotentByAbelianByFinite
2.4 Examples
2.4-1 PolExamples
3 An example application
3.1 Presentation for rational matrix groups
3.2 Modules series
3.3 Triangularizable subgroups
4 Installation
4.1 Installing this package
4.2 Loading the Polenta package
4.3 Running the test suite
5 Information Messages
5.1 Info Class
5.1-1 InfoPolenta
5.2 Example
References
Index
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