  
  
                                   [1X ModIsom [101X
  
  
      [1X Computing automorphisms and checking isomorphisms for modular group
                          algebras of finite p-groups [101X
  
  
                                     3.2.0
  
  
                                 6 October 2026
  
  
                                  Bettina Eick
  
                               Diego Garcia-Lucas
  
                                  Leo Margolis
  
                                  Tobias Moede
  
  
  
  Bettina Eick
      Email:    [7Xmailto:beick@tu-bs.de[107X
      Homepage: [7Xhttp://www.iaa.tu-bs.de/beick[107X
      Address:  [33X[0;14YInstitut Analysis und Algebra[133X
                [33X[0;14YTU Braunschweig[133X
                [33X[0;14YUniversitätsplatz 2[133X
                [33X[0;14YD-38106 Braunschweig[133X
                [33X[0;14YGermany[133X
  
  
  Diego Garcia-Lucas
      Email:    [7Xmailto:diego.garcial@usc.es[107X
      Address:  [33X[0;14YDepartamento de Matematicas[133X
                [33X[0;14YFacultad de Matematicas[133X
                [33X[0;14YUniversidad de Santiago de Compostela[133X
                [33X[0;14YRua   de   Lope  Gomez  de  Marzoa,  s/nES-15705  Santiago  de
                Compostela[133X
                [33X[0;14YSpain[133X
  
  
  Leo Margolis
      Email:    [7Xmailto:leo.margolis@uam.es[107X
      Homepage: [7Xhttp://www.margollo.github.io[107X
      Address:  [33X[0;14YDepartamento de Matematicas[133X
                [33X[0;14YUniversidad Autonoma de Madrid[133X
                [33X[0;14YCampus Cantoblanco[133X
                [33X[0;14Y28049 Madrid[133X
                [33X[0;14YSpain[133X
  
  
  Tobias Moede
      Email:    [7Xmailto:t.moede@tu-braunschweig.de[107X
      Homepage: [7Xhttps://www.tu-braunschweig.de/iaa/personal/moede[107X
      Address:  [33X[0;14YInstitute of Analysis and Algebra[133X
                [33X[0;14YTU Braunschweig[133X
                [33X[0;14YUniversitaetsplatz 2, 38106 Braunschweig[133X
                [33X[0;14YGermany[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (ModIsom)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YAssociative algebras and nilpotency[133X
    1.2 [33X[0;0YIsomorphisms and Automorphisms[133X
    1.3 [33X[0;0YThe Modular Isomorphism Problem (MIP)[133X
    1.4 [33X[0;0YA nilpotent quotient algorithm[133X
    1.5 [33X[0;0YKurosh Algebras[133X
  2 [33X[0;0YTables[133X
    2.1 [33X[0;0YNilpotent tables[133X
      2.1-1 GetEntryTable
      2.1-2 MultByTable
      2.1-3 CompareTables
      2.1-4 CheckAssociativity
      2.1-5 CheckCommutativity
      2.1-6 CheckConsistency
    2.2 [33X[0;0YAlgebras in the GAP sense[133X
      2.2-1 AlgebraByTable
      2.2-2 NilpotentTableOfRad
    2.3 [33X[0;0YTables for the Modular Isomorphism Problem[133X
      2.3-1 TableOfRadQuotient
      2.3-2 ModIsomTable
      2.3-3 MIPElementTableToAlgebra
      2.3-4 MIPElementAlgebraToTable
  3 [33X[0;0YAutomorphism groups and Canonical Forms[133X
    3.1 [33X[0;0YAutomorphism groups[133X
      3.1-1 AutGroupOfTable
    3.2 [33X[0;0YCanonical forms[133X
      3.2-1 CanonicalFormOfTable
      3.2-2 CanoFormWithAutGroupOfTable
    3.3 [33X[0;0YExample of canonical form computation[133X
  4 [33X[0;0YThe modular isomorphism problem[133X
    4.1 [33X[0;0YComputing bins and checking bins[133X
      4.1-1 BinsByGT
      4.1-2 MIPSplitGroupsByGroupTheoreticalInvariants
      4.1-3 MIPSplitGroupsByGroupTheoreticalInvariantsNoCohomology
      4.1-4 BinsByGTAllFields
      4.1-5 MIPSplitGroupsByAlgebras
      4.1-6 MIPBinSplit
    4.2 [33X[0;0YKernel size[133X
      4.2-1 KernelSizePowerMap
    4.3 [33X[0;0YThe group theoretical invariants[133X
      4.3-1 GroupInfo
      4.3-2 CenterDerivedInfo
      4.3-3 SandlingInfo
      4.3-4 JenningsInfo
      4.3-5 JenningsDerivedInfo
      4.3-6 BaginskiInfo
      4.3-7 BaginskiCarantiInfo
      4.3-8 NilpotencyClassInfo
      4.3-9 Theorem41MS22
      4.3-10 CyclicDerivedInfo
      4.3-11 MaximalAbelianDirectFactor
      4.3-12 SuccessorsN
      4.3-13 CanonicalNormalSubgroups
      4.3-14 NormalSubgroupsInfo
      4.3-15 IsCoveredByTheory
      4.3-16 DimensionTwoCohomology
      4.3-17 ConjugacyClassInfo
      4.3-18 SubgroupsInfo
  5 [33X[0;0YNilpotent Quotients[133X
    5.1 [33X[0;0YComputing nilpotent quotients[133X
      5.1-1 NilpotentQuotientOfFpAlgebra
    5.2 [33X[0;0YExample of nilpotent quotient computation[133X
  6 [33X[0;0YRelatively free Algebras[133X
    6.1 [33X[0;0YComputing Kurosh Algebras[133X
      6.1-1 KuroshAlgebra
      6.1-2 ExpandExponentLaw
    6.2 [33X[0;0YA Library of Kurosh Algebras[133X
      6.2-1 KuroshAlgebraByLib
    6.3 [33X[0;0YExample of accessing the library of Kurosh algebras[133X
  
  
  [32X
