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ANUPQ

ANU p-Quotient

3.2.6

7 March 2022

Greg Gamble
Email: Greg.Gamble@uwa.edu.au
Homepage: http://school.maths.uwa.edu.au/~gregg
Address:
Department of Mathematics and Statistics
Curtin University
GPO Box U 1987
Perth WA 6845
Australia

Werner Nickel
Homepage: https://www2.mathematik.tu-darmstadt.de/~nickel/

Eamonn O'Brien
Email: obrien@math.auckland.ac.nz
Homepage: https://www.math.auckland.ac.nz/~obrien
Address:
Department of Mathematics
University of Auckland
Private Bag 92019
Auckland
New Zealand

Copyright

© 2001-2016 by Greg Gamble

© 2001-2005 by Werner Nickel

© 1995-2001 by Eamon O'Brien

The GAP package ANUPQ is licensed under the Artistic License 2.0.

Contents

1.2 How to read this manual

1.3 Authors and Acknowledgements

2 Mathematical Background and Terminology

2.1 Basic notions

  2.1-1 pc Presentations and Consistency
  2.1-2 Exponent-p Central Series and Weighted pc Presentations
  2.1-3 p-Cover, p-Multiplicator
  2.1-4 Descendants, Capable, Terminal, Nucleus
  2.1-5 Laws

2.2 The p-quotient Algorithm

  2.2-1 Finding the p-cover
  2.2-2 Imposing the Relations of the fp Group
  2.2-3 Imposing Laws

2.3 The p-group generation Algorithm, Standard Presentation, Isomorphism Testing

3 Infrastructure

3.1 Loading the ANUPQ Package

3.2 The ANUPQData Record

3.2-1 ANUPQData
3.2-2 ANUPQDirectoryTemporary

3.3 Setting the Verbosity of ANUPQ via Info and InfoANUPQ

3.3-1 InfoANUPQ

3.4 Utility Functions

  3.4-1 PqLeftNormComm
  3.4-2 PqGAPRelators
  3.4-3 PqParseWord
  3.4-4 PqExample
  3.4-5 AllPqExamples
  3.4-6 GrepPqExamples
  3.4-7 ToPQLog

3.5 Attributes and a Property for fp and pc p-groups

3.5-1 NuclearRank

3.6 Hints and Warnings regarding the use of Options

3.6-1 ANUPQWarnOfOtherOptions

4 Non-interactive ANUPQ functions

4.1 Computing p-Quotients

  4.1-1 Pq
  4.1-2 PqEpimorphism
  4.1-3 PqPCover

4.2 Computing Standard Presentations

4.2-1 PqStandardPresentation
4.2-2 EpimorphismPqStandardPresentation

4.3 Testing p-Groups for Isomorphism

4.3-1 IsPqIsomorphicPGroup

4.4 Computing Descendants of a p-Group

  4.4-1 PqDescendants
  4.4-2 PqSupplementInnerAutomorphisms
  4.4-3 PqList
  4.4-4 SavePqList

5 Interactive ANUPQ functions

5.1 Starting and Stopping Interactive ANUPQ Processes

  5.1-1 PqStart
  5.1-2 PqQuit
  5.1-3 PqQuitAll

5.2 Interactive ANUPQ Process Utility Functions

  5.2-1 PqProcessIndex
  5.2-2 PqProcessIndices
  5.2-3 IsPqProcessAlive

5.3 Interactive Versions of Non-interactive ANUPQ Functions

  5.3-1 Pq
  5.3-2 PqEpimorphism
  5.3-3 PqPCover
  5.3-4 PqStandardPresentation
  5.3-5 EpimorphismPqStandardPresentation
  5.3-6 PqDescendants
  5.3-7 PqSetPQuotientToGroup

5.4 Low-level Interactive ANUPQ functions based on menu items of the pq program

5.5 General commands

  5.5-1 PqNrPcGenerators
  5.5-2 PqFactoredOrder
  5.5-3 PqOrder
  5.5-4 PqPClass
  5.5-5 PqWeight
  5.5-6 PqCurrentGroup
  5.5-7 PqDisplayPcPresentation
  5.5-8 PqSetOutputLevel
  5.5-9 PqEvaluateIdentities

5.6 Commands from the Main p-Quotient menu

  5.6-1 PqPcPresentation
  5.6-2 PqSavePcPresentation
  5.6-3 PqRestorePcPresentation
  5.6-4 PqNextClass
  5.6-5 PqComputePCover

5.8 Commands from the Standard Presentation menu

  5.8-1 PqSPComputePcpAndPCover
  5.8-2 PqSPStandardPresentation
  5.8-3 PqSPSavePresentation
  5.8-4 PqSPCompareTwoFilePresentations
  5.8-5 PqSPIsomorphism

5.9 Commands from the Main p-Group Generation menu

  5.9-1 PqPGSupplyAutomorphisms
  5.9-2 PqPGExtendAutomorphisms
  5.9-3 PqPGConstructDescendants
  5.9-4 PqPGSetDescendantToPcp

5.10 Commands from the Advanced p-Group Generation menu

  5.10-1 PqAPGDegree
  5.10-2 PqAPGPermutations
  5.10-3 PqAPGOrbits
  5.10-4 PqAPGOrbitRepresentatives
  5.10-5 PqAPGSingleStage

5.11 Primitive Interactive ANUPQ Process Read/Write Functions

  5.11-1 PqRead
  5.11-2 PqReadAll
  5.11-3 PqReadUntil
  5.11-4 PqWrite

6 ANUPQ Options

6.1-1 AllANUPQoptions
6.1-2 ANUPQoptions

6.2 Detailed descriptions of ANUPQ Options

7 Installing the ANUPQ Package

7.1 Testing your ANUPQ installation

7.2 Running the pq program as a standalone

A.1 The Relators Option

A.2 The Identities Option and PqEvaluateIdentities Function

A.3 A Large Example

A.4 Developing descendants trees

A.4-1 PqDescendantsTreeCoclassOne

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