  
  
                                   [1X LiePRing [101X
  
  
                   [1X Database and algorithms for Lie p-rings [101X
  
  
                                     2.9.3
  
  
                                 18 August 2026
  
  
                                  Bettina Eick
  
                              Michael Vaughan-Lee
  
  
  
  Bettina Eick
      Email:    [7Xmailto:beick@tu-bs.de[107X
      Homepage: [7Xhttp://www.iaa.tu-bs.de/beick[107X
  Michael Vaughan-Lee
      Email:    [7Xmailto:michael.vaughan-lee@chch.ox.ac.uk[107X
      Homepage: [7Xhttp://users.ox.ac.uk/~vlee[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0Y[5XLiePRing[105X gives access to the database of Lie [22Xp[122X-rings of order at most [22Xp^7[122X as
  determined  by  Mike  Newman,  Eamonn  O'Brien  and Michael Vaughan-Lee, see
  [NOV03]  and  [OV05],  and it provides some functionality to work with these
  Lie [22Xp[122X-rings.[133X
  
  [33X[0;0YIf  you  use  [5XLiePRing[105X,  then  please  cite  it as: [13XBettina Eick and Michael
  Vaughan-Lee[113X,  LiePRing  --  A  GAP  Package for computing with nilpotent Lie
  rings         of         prime-power         order        (2014),        see
  [7Xhttps://www.gap-system.org/Packages/liepring.html[107X[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y[5XLiePRing[105X  is  free  software; you can redistribute it under the terms of the
  GNU   General   Public  License  ([7Xhttps://www.fsf.org/licenses/gpl.html[107X)  as
  published  by the Free Software Foundation; either version 2 of the License,
  or  (at  your option) any later version. [5XLiePRing[105X is distributed in the hope
  that  it  will be useful, but WITHOUT ANY WARRANTY; without even the implied
  warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe  Lazard  correspondence  induces a one-to-one correspondence between the
  Lie [22Xp[122X-rings of order [22Xp^n[122X and class less than [22Xp[122X and the [22Xp[122X-groups of order [22Xp^n[122X
  and  class  less  than  [22Xp[122X.  [5XLiePRing[105X  provides  a  function to evaluate this
  correspondence; this function has been implemented and given to us by Willem
  de Graaf.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (LiePRing)[101X
  
  1 [33X[0;0YLie [22Xp[122X-rings[133X
  2 [33X[0;0YLiePRings in GAP[133X
    2.1 [33X[0;0YOrdinary Lie [22Xp[122X-rings[133X
      2.1-1 LiePRingBySCTable
      2.1-2 CheckIsLiePRing
    2.2 [33X[0;0YGeneric Lie [22Xp[122X-rings[133X
      2.2-1 IndeterminateByName
    2.3 [33X[0;0YSpecialising Lie [22Xp[122X-rings[133X
      2.3-1 SpecialiseLiePRing
      2.3-2 SpecialisePrimeOfLiePRing
      2.3-3 LiePValues
    2.4 [33X[0;0YSubrings of Lie [22Xp[122X-rings[133X
      2.4-1 LiePSubring
      2.4-2 LiePIdeal
      2.4-3 LiePQuotient
    2.5 [33X[0;0YElementary functions[133X
      2.5-1 PrimeOfLiePRing
      2.5-2 BasisOfLiePRing
      2.5-3 DimensionOfLiePRing
      2.5-4 ParametersOfLiePRing
      2.5-5 ViewPCPresentation
    2.6 [33X[0;0YSeries of subrings[133X
      2.6-1 LiePLowerCentralSeries
      2.6-2 LiePLowerPCentralSeries
      2.6-3 LiePDerivedSeries
      2.6-4 LiePMinimalGeneratingSet
    2.7 [33X[0;0YThe Lazard correspondence[133X
      2.7-1 PGroupByLiePRing
  3 [33X[0;0YThe Database[133X
    3.1 [33X[0;0YAccessing Lie [22Xp[122X-rings[133X
      3.1-1 LiePRingsByLibrary
      3.1-2 LiePRingsByLibrary
    3.2 [33X[0;0YNumbers of Lie [22Xp[122X-rings[133X
      3.2-1 NumberOfLiePRings
      3.2-2 NumberOfLiePRings
      3.2-3 NumberOfLiePRingsInFamily
    3.3 [33X[0;0YSearching the database[133X
      3.3-1 LiePRingsInFamily
    3.4 [33X[0;0YMore details[133X
      3.4-1 LibraryName
      3.4-2 ShortPresentation
      3.4-3 LibraryConditions
      3.4-4 MinimalGeneratorNumberOfLiePRing
      3.4-5 PClassOfLiePRing
    3.5 [33X[0;0YSpecial functions for dimension 7[133X
      3.5-1 LiePRingsDim7ByFile
      3.5-2 LiePRingsDim7ByFile
    3.6 [33X[0;0YDimension 8 and maximal class[133X
      3.6-1 LiePRingsByLibraryMC8
      3.6-2 LiePRingsInFamilyMC8
  4 [33X[0;0YAdvanced functions for Lie [22Xp[122X-rings[133X
    4.1 [33X[0;0YSchur multipliers[133X
      4.1-1 LiePSchurMult
      4.1-2 ElementNumbers
    4.2 [33X[0;0YAutomorphism groups[133X
      4.2-1 AutGroupDescription
  
  
  [32X
