  
  
                                    [1X ANUPQ [101X
  
  
                                [1X ANU p-Quotient [101X
  
  
                                     3.2.6
  
  
                                  7 March 2022
  
  
                                  Greg Gamble
  
                                 Werner Nickel
  
                                 Eamonn O'Brien
  
  
  
  Greg Gamble
      Email:    [7Xmailto:Greg.Gamble@uwa.edu.au[107X
      Homepage: [7Xhttp://school.maths.uwa.edu.au/~gregg[107X
      Address:  [33X[0;14YDepartment of Mathematics and Statistics[133X
                [33X[0;14YCurtin University[133X
                [33X[0;14YGPO Box U 1987[133X
                [33X[0;14YPerth WA 6845[133X
                [33X[0;14YAustralia[133X
  
  
  Werner Nickel
      Homepage: [7Xhttps://www2.mathematik.tu-darmstadt.de/~nickel/[107X
  Eamonn O'Brien
      Email:    [7Xmailto:obrien@math.auckland.ac.nz[107X
      Homepage: [7Xhttps://www.math.auckland.ac.nz/~obrien[107X
      Address:  [33X[0;14YDepartment of Mathematics[133X
                [33X[0;14YUniversity of Auckland[133X
                [33X[0;14YPrivate Bag 92019[133X
                [33X[0;14YAuckland[133X
                [33X[0;14YNew Zealand[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2001-2016 by Greg Gamble[133X
  
  [33X[0;0Y© 2001-2005 by Werner Nickel[133X
  
  [33X[0;0Y© 1995-2001 by Eamon O'Brien[133X
  
  [33X[0;0YThe   [5XGAP[105X   package  [5XANUPQ[105X  is  licensed  under  the  Artistic  License  2.0
  ([7Xhttps://opensource.org/licenses/artistic-license-2.0[107X).[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (ANUPQ)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview[133X
    1.2 [33X[0;0YHow to read this manual[133X
    1.3 [33X[0;0YAuthors and Acknowledgements[133X
  2 [33X[0;0YMathematical Background and Terminology[133X
    2.1 [33X[0;0YBasic notions[133X
      2.1-1 [33X[0;0Ypc Presentations and Consistency[133X
      2.1-2 [33X[0;0YExponent-[22Xp[122X Central Series and Weighted pc Presentations[133X
      2.1-3 [33X[0;0Y[22Xp[122X-Cover, [22Xp[122X-Multiplicator[133X
      2.1-4 [33X[0;0YDescendants, Capable, Terminal, Nucleus[133X
      2.1-5 [33X[0;0YLaws[133X
    2.2 [33X[0;0YThe p-quotient Algorithm[133X
      2.2-1 [33X[0;0YFinding the [22Xp[122X-cover[133X
      2.2-2 [33X[0;0YImposing the Relations of the fp Group[133X
      2.2-3 [33X[0;0YImposing Laws[133X
    2.3 [33X[0;0YThe p-group generation Algorithm, Standard Presentation, Isomorphism
    Testing[133X
  3 [33X[0;0YInfrastructure[133X
    3.1 [33X[0;0YLoading the ANUPQ Package[133X
    3.2 [33X[0;0YThe ANUPQData Record[133X
      3.2-1 ANUPQData
      3.2-2 ANUPQDirectoryTemporary
    3.3 [33X[0;0YSetting the Verbosity of ANUPQ via Info and InfoANUPQ[133X
      3.3-1 InfoANUPQ
    3.4 [33X[0;0YUtility Functions[133X
      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 [33X[0;0YAttributes and a Property for fp and pc p-groups[133X
      3.5-1 NuclearRank
    3.6 [33X[0;0YHints and Warnings regarding the use of Options[133X
      3.6-1 ANUPQWarnOfOtherOptions
  4 [33X[0;0YNon-interactive ANUPQ functions[133X
    4.1 [33X[0;0YComputing p-Quotients[133X
      4.1-1 Pq
      4.1-2 PqEpimorphism
      4.1-3 PqPCover
    4.2 [33X[0;0YComputing Standard Presentations[133X
      4.2-1 PqStandardPresentation
      4.2-2 EpimorphismPqStandardPresentation
    4.3 [33X[0;0YTesting p-Groups for Isomorphism[133X
      4.3-1 IsPqIsomorphicPGroup
    4.4 [33X[0;0YComputing Descendants of a p-Group[133X
      4.4-1 PqDescendants
      4.4-2 PqSupplementInnerAutomorphisms
      4.4-3 PqList
      4.4-4 SavePqList
  5 [33X[0;0YInteractive ANUPQ functions[133X
    5.1 [33X[0;0YStarting and Stopping Interactive ANUPQ Processes[133X
      5.1-1 PqStart
      5.1-2 PqQuit
      5.1-3 PqQuitAll
    5.2 [33X[0;0YInteractive ANUPQ Process Utility Functions[133X
      5.2-1 PqProcessIndex
      5.2-2 PqProcessIndices
      5.2-3 IsPqProcessAlive
    5.3 [33X[0;0YInteractive Versions of Non-interactive ANUPQ Functions[133X
      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 [33X[0;0YLow-level Interactive ANUPQ functions based on menu items of the pq
    program[133X
    5.5 [33X[0;0YGeneral commands[133X
      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 [33X[0;0YCommands from the Main [22Xp[122X-Quotient menu[133X
      5.6-1 PqPcPresentation
      5.6-2 PqSavePcPresentation
      5.6-3 PqRestorePcPresentation
      5.6-4 PqNextClass
      5.6-5 PqComputePCover
    5.7 [33X[0;0YCommands from the Advanced [22Xp[122X-Quotient menu[133X
      5.7-1 PqCollect
      5.7-2 PqSolveEquation
      5.7-3 PqCommutator
      5.7-4 PqSetupTablesForNextClass
      5.7-5 PqTails
      5.7-6 PqComputeTails
      5.7-7 PqAddTails
      5.7-8 PqDoConsistencyChecks
      5.7-9 PqCollectDefiningRelations
      5.7-10 PqCollectWordInDefiningGenerators
      5.7-11 PqCommutatorDefiningGenerators
      5.7-12 PqDoExponentChecks
      5.7-13 PqEliminateRedundantGenerators
      5.7-14 PqRevertToPreviousClass
      5.7-15 PqSetMaximalOccurrences
      5.7-16 PqSetMetabelian
      5.7-17 PqDoConsistencyCheck
      5.7-18 PqCompact
      5.7-19 PqEchelonise
      5.7-20 PqSupplyAutomorphisms
      5.7-21 PqExtendAutomorphisms
      5.7-22 PqApplyAutomorphisms
      5.7-23 PqDisplayStructure
      5.7-24 PqDisplayAutomorphisms
      5.7-25 PqWritePcPresentation
    5.8 [33X[0;0YCommands from the Standard Presentation menu[133X
      5.8-1 PqSPComputePcpAndPCover
      5.8-2 PqSPStandardPresentation
      5.8-3 PqSPSavePresentation
      5.8-4 PqSPCompareTwoFilePresentations
      5.8-5 PqSPIsomorphism
    5.9 [33X[0;0YCommands from the Main [22Xp[122X-Group Generation menu[133X
      5.9-1 PqPGSupplyAutomorphisms
      5.9-2 PqPGExtendAutomorphisms
      5.9-3 PqPGConstructDescendants
      5.9-4 PqPGSetDescendantToPcp
    5.10 [33X[0;0YCommands from the Advanced [22Xp[122X-Group Generation menu[133X
      5.10-1 PqAPGDegree
      5.10-2 PqAPGPermutations
      5.10-3 PqAPGOrbits
      5.10-4 PqAPGOrbitRepresentatives
      5.10-5 PqAPGSingleStage
    5.11 [33X[0;0YPrimitive Interactive ANUPQ Process Read/Write Functions[133X
      5.11-1 PqRead
      5.11-2 PqReadAll
      5.11-3 PqReadUntil
      5.11-4 PqWrite
  6 [33X[0;0YANUPQ Options[133X
    6.1 [33X[0;0YOverview[133X
      6.1-1 AllANUPQoptions
      6.1-2 ANUPQoptions
    6.2 [33X[0;0YDetailed descriptions of ANUPQ Options[133X
  7 [33X[0;0YInstalling the ANUPQ Package[133X
    7.1 [33X[0;0YTesting your ANUPQ installation[133X
    7.2 [33X[0;0YRunning the pq program as a standalone[133X
  A [33X[0;0YExamples[133X
    A.1 [33X[0;0YThe Relators Option[133X
    A.2 [33X[0;0YThe Identities Option and PqEvaluateIdentities Function[133X
    A.3 [33X[0;0YA Large Example[133X
    A.4 [33X[0;0YDeveloping descendants trees[133X
      A.4-1 PqDescendantsTreeCoclassOne
  
  
  [32X
