  
  
                                     [1X[5XPERMUT[105X[101X
  
  
                   [1XA [5XGAP[105X4 package to deal with permutability[101X
  
  
                                 Version 2.0.4
  
  
                           Adolfo Ballester-Bolinches
  
                               Enric Cosme-Llópez
  
                              Ramón Esteban-Romero
  
  
  
  Adolfo Ballester-Bolinches
      Email:    [7Xmailto:Adolfo.Ballester@uv.es[107X
      Address:  [33X[0;14YDepartament de Matemàtiques, Universitat de València[133X
  
  
  Enric Cosme-Llópez
      Email:    [7Xmailto:Enric.Cosme@uv.es[107X
      Homepage: [7Xhttps://www.uv.es/coslloen/[107X
      Address:  [33X[0;14YDepartament de Matemàtiques, Universitat de València[133X
  
  
  Ramón Esteban-Romero
      Email:    [7Xmailto:Ramon.Esteban@uv.es[107X
      Homepage: [7Xhttps://www.uv.es/estebanr/[107X
      Address:  [33X[0;14YDepartament de Matemàtiques, Universitat de València[133X
  
  
  
  -------------------------------------------------------
  
  
  [1XContents (PERMUT)[101X
  
  1 [33X[0;0YIntroduction to the [5XPERMUT[105X Package[133X
  2 [33X[0;0YInstallation and Help of the [5XPERMUT[105X Package[133X
  3 [33X[0;0YPermutability of Subgroups in Finite Groups[133X
    3.1 [33X[0;0YPermutability functions[133X
      3.1-1 ArePermutableSubgroups
    3.2 [33X[0;0YEmbedding properties related to permutability[133X
      3.2-1 PermutMaxTries
      3.2-2 IsPermutable
      3.2-3 OneSubgroupNotPermutingWith
      3.2-4 IsFPermutable
      3.2-5 OneFSubgroupNotPermutingWith
      3.2-6 IsSPermutable
      3.2-7 OneSylowSubgroupNotPermutingWith
      3.2-8 IsSNPermutable
      3.2-9 OneSystemNormaliserNotPermutingWith
      3.2-10 IsConjugatePermutable
      3.2-11 OneConjugateSubgroupNotPermutingWith
      3.2-12 IsWeaklySPermutable
      3.2-13 OneElementShowingNotWeaklySPermutable
      3.2-14 IsWeaklyPermutable
      3.2-15 OneElementShowingNotWeaklyPermutable
      3.2-16 IsWeaklyNormal
      3.2-17 OneElementShowingNotWeaklyNormal
      3.2-18 IsWithSubnormalizerCondition
      3.2-19 OneSubgroupInWhichSubnormalNotNormal
      3.2-20 IsWithSubpermutizerCondition
      3.2-21 OneSubgroupInWhichSubnormalNotPermutable
      3.2-22 IsWithSSubpermutizerCondition
      3.2-23 OneSubgroupInWhichSubnormalNotSPermutable
  4 [33X[0;0YT-groups, PT-groups, and PST-groups[133X
    4.1 [33X[0;0Y[21XOne[121X functions[133X
      4.1-1 OneSubnormalNonNormalSubgroup
      4.1-2 OneSubnormalNonPermutableSubgroup
      4.1-3 OneSubnormalNonSPermutableSubgroup
      4.1-4 OneSubnormalNonConjugatePermutableSubgroup
      4.1-5 OneSubnormalNonSNPermutableSubgroup
    4.2 [33X[0;0YGroup properties related to permutability[133X
      4.2-1 IsTGroup
      4.2-2 IsPTGroup
      4.2-3 IsPSTGroup
      4.2-4 IsCPTGroup
      4.2-5 IsPSNTGroup
  5 [33X[0;0YLocal Functions in the [5XPERMUT[105X Package[133X
    5.1 [33X[0;0YA Local Function for Supersolubility[133X
      5.1-1 IsPSupersolvable
    5.2 [33X[0;0YLocal functions for T-groups, PT-groups, and PST-groups[133X
      5.2-1 IsCp
      5.2-2 IsXp
      5.2-3 IsYp
    5.3 [33X[0;0YAuxiliary Functions for T-groups, PT-groups, and PST-groups[133X
      5.3-1 IsAbCp
      5.3-2 IsDedekindSylow
      5.3-3 IwasawaTripleWithSubgroup
      5.3-4 IwasawaTriple
      5.3-5 IsIwasawaSylow
  6 [33X[0;0YTotally and Mutually Permutable Products[133X
    6.1 [33X[0;0YFunctions for Mutually and Totally Permutable Products[133X
      6.1-1 AreMutuallyPermutableSubgroups
      6.1-2 OnePairShowingNotMutuallyPermutableSubgroups
      6.1-3 AreTotallyPermutableSubgroups
      6.1-4 OnePairShowingNotTotallyPermutableSubgroups
      6.1-5 AreMutuallyFPermutableSubgroups
      6.1-6 OnePairShowingNotMutuallyFPermutableSubgroups
      6.1-7 AreTotallyFPermutableSubgroups
      6.1-8 OnePairShowingNotTotallyFPermutableSubgroups
  7 [33X[0;0YOther Functions in the [5XPERMUT[105X Package[133X
    7.1 [33X[0;0YFunctions[133X
      7.1-1 AllSubnormalSubgroups
      7.1-2 PrimesDividingSize
      7.1-3 SylowSubgroups
      7.1-4 IsSCGroup
      7.1-5 IsSylowTowerGroup
      7.1-6 Permutizer
      7.1-7 AllGeneratorsCyclicPGroup
  
  
  [32X
