#SIXFORMAT  GapDocGAP
HELPBOOKINFOSIXTMP := rec(
encoding := "UTF-8",
bookname := "permut",
entries :=
[ [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", "X7D2C85EC87DD46E5" ],
  [ "Table of Contents", ".-1", [ 0, 0, 1 ], 41, 2, "table of contents", 
      "X8537FEB07AF2BEC8" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YIntroduction to the \033[5XPERMUT\033[105X\033[10\
1X\027\033[1X\027 Package\033[133X\033[101X", "1", [ 1, 0, 0 ], 1, 3, 
      "introduction to the permut package", "X7A6D71137AE20820" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YInstallation and Help of the \033[5XPERMUT\033[10\
5X\033[101X\027\033[1X\027 Package\033[133X\033[101X", "2", [ 2, 0, 0 ], 1, 
      5, "installation and help of the permut package", "X78FA2A627FAD92E6" ],
  [ "\033[1X\033[33X\033[0;-2YPermutability of Subgroups in Finite Groups\033[\
133X\033[101X", "3", [ 3, 0, 0 ], 1, 6, 
      "permutability of subgroups in finite groups", "X7B87CECD83EA77DF" ], 
  [ "\033[1X\033[33X\033[0;-2YPermutability functions\033[133X\033[101X", 
      "3.1", [ 3, 1, 0 ], 11, 6, "permutability functions", 
      "X834D77E17960C0B7" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YEmbedding properties related to permutability\\
033[133X\033[101X", "3.2", [ 3, 2, 0 ], 54, 7, 
      "embedding properties related to permutability", "X875BEB9B7D0DBC9A" ], 
  [ "\033[1X\033[33X\033[0;-2YT-groups, PT-groups, and PST-groups\033[133X\033\
[101X", "4", [ 4, 0, 0 ], 1, 15, "t-groups pt-groups and pst-groups", 
      "X7E7EFDD1878F599D" ], 
  [ 
      "\033[1X\033[33X\033[0;-2Y\033[21XOne\033[121X\033[101X\027\033[1X\027 func\
tions\033[133X\033[101X", "4.1", [ 4, 1, 0 ], 25, 15, "one functions", 
      "X7ABC289380DB85BE" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YGroup properties related to permutability\033[133\
X\033[101X", "4.2", [ 4, 2, 0 ], 159, 17, 
      "group properties related to permutability", "X7B13DA0A800D8635" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YLocal Functions in the \033[5XPERMUT\033[105X\\
033[101X\027\033[1X\027 Package\033[133X\033[101X", "5", [ 5, 0, 0 ], 1, 21, 
      "local functions in the permut package", "X83F7986D84F33F6C" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YA Local Function for Supersolubility\033[133X\\
033[101X", "5.1", [ 5, 1, 0 ], 15, 21, "a local function for supersolubility",
      "X7E8389FD7DE9769C" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YLocal functions for T-groups, PT-groups, and PST-\
groups\033[133X\033[101X", "5.2", [ 5, 2, 0 ], 62, 22, 
      "local functions for t-groups pt-groups and pst-groups", 
      "X7C4B2A9A7F2D7E0B" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YAuxiliary Functions for T-groups, PT-groups, and \
PST-groups\033[133X\033[101X", "5.3", [ 5, 3, 0 ], 161, 23, 
      "auxiliary functions for t-groups pt-groups and pst-groups", 
      "X8540D4B679519F8B" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YTotally and Mutually Permutable Products\033[133X\
\033[101X", "6", [ 6, 0, 0 ], 1, 27, 
      "totally and mutually permutable products", "X82E82E45786E1B22" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YFunctions for Mutually and Totally Permutable Pro\
ducts\033[133X\033[101X", "6.1", [ 6, 1, 0 ], 18, 27, 
      "functions for mutually and totally permutable products", 
      "X85291E9D86736F21" ], 
  [ 
      "\033[1X\033[33X\033[0;-2YOther Functions in the \033[5XPERMUT\033[105X\\
033[101X\027\033[1X\027 Package\033[133X\033[101X", "7", [ 7, 0, 0 ], 1, 30, 
      "other functions in the permut package", "X840872AB823EB3DB" ], 
  [ "\033[1X\033[33X\033[0;-2YFunctions\033[133X\033[101X", "7.1", 
      [ 7, 1, 0 ], 8, 30, "functions", "X86FA580F8055B274" ], 
  [ "Bibliography", "bib", [ "Bib", 0, 0 ], 1, 33, "bibliography", 
      "X7A6F98FD85F02BFE" ], 
  [ "References", "bib", [ "Bib", 0, 0 ], 1, 33, "references", 
      "X7A6F98FD85F02BFE" ], 
  [ "Index", "ind", [ "Ind", 0, 0 ], 1, 35, "index", "X83A0356F839C696F" ], 
  [ "\033[2XArePermutableSubgroups\033[102X", "3.1-1", [ 3, 1, 1 ], 14, 6, 
      "arepermutablesubgroups", "X862727A87C26B10B" ], 
  [ "\033[2XPermutMaxTries\033[102X", "3.2-1", [ 3, 2, 1 ], 64, 7, 
      "permutmaxtries", "X85CFBEBB83245E3A" ], 
  [ "\033[2XIsPermutable\033[102X", "3.2-2", [ 3, 2, 2 ], 73, 7, 
      "ispermutable", "X80C15D427EC11A5F" ], 
  [ "\033[2XIsPermutableInParent\033[102X", "3.2-2", [ 3, 2, 2 ], 73, 7, 
      "ispermutableinparent", "X80C15D427EC11A5F" ], 
  [ "\033[2XOneSubgroupNotPermutingWith\033[102X", "3.2-3", [ 3, 2, 3 ], 91, 
      7, "onesubgroupnotpermutingwith", "X8244918D7D1C2703" ], 
  [ "\033[2XOneSubgroupNotPermutingWithInParent\033[102X", "3.2-3", 
      [ 3, 2, 3 ], 91, 7, "onesubgroupnotpermutingwithinparent", 
      "X8244918D7D1C2703" ], 
  [ "\033[2XIsFPermutable\033[102X", "3.2-4", [ 3, 2, 4 ], 143, 8, 
      "isfpermutable", "X865C7F81823FFA10" ], 
  [ "\033[2XOneFSubgroupNotPermutingWith\033[102X", "3.2-5", [ 3, 2, 5 ], 
      156, 9, "onefsubgroupnotpermutingwith", "X826D28757824F83E" ], 
  [ "\033[2XIsSPermutable\033[102X", "3.2-6", [ 3, 2, 6 ], 204, 9, 
      "isspermutable", "X7BA6690983912C09" ], 
  [ "\033[2XIsSPermutableInParent\033[102X", "3.2-6", [ 3, 2, 6 ], 204, 9, 
      "isspermutableinparent", "X7BA6690983912C09" ], 
  [ "\033[2XOneSylowSubgroupNotPermutingWith\033[102X", "3.2-7", [ 3, 2, 7 ], 
      221, 10, "onesylowsubgroupnotpermutingwith", "X83E103AF7C3DC9B7" ], 
  [ "\033[2XOneSylowSubgroupNotPermutingWithInParent\033[102X", "3.2-7", 
      [ 3, 2, 7 ], 221, 10, "onesylowsubgroupnotpermutingwithinparent", 
      "X83E103AF7C3DC9B7" ], 
  [ "\033[2XIsSNPermutable\033[102X", "3.2-8", [ 3, 2, 8 ], 238, 10, 
      "issnpermutable", "X86A62A52831BE00E" ], 
  [ "\033[2XIsSNPermutableInParent\033[102X", "3.2-8", [ 3, 2, 8 ], 238, 10, 
      "issnpermutableinparent", "X86A62A52831BE00E" ], 
  [ "\033[2XOneSystemNormaliserNotPermutingWith\033[102X", "3.2-9", 
      [ 3, 2, 9 ], 247, 10, "onesystemnormalisernotpermutingwith", 
      "X83D1BF5778D6790A" ], 
  [ "\033[2XOneSystemNormaliserNotPermutingWithInParent\033[102X", "3.2-9", 
      [ 3, 2, 9 ], 247, 10, "onesystemnormalisernotpermutingwithinparent", 
      "X83D1BF5778D6790A" ], 
  [ "\033[2XIsConjugatePermutable\033[102X", "3.2-10", [ 3, 2, 10 ], 273, 11, 
      "isconjugatepermutable", "X7B2E052E7F9C4251" ], 
  [ "\033[2XIsConjugatePermutableInParent\033[102X", "3.2-10", [ 3, 2, 10 ], 
      273, 11, "isconjugatepermutableinparent", "X7B2E052E7F9C4251" ], 
  [ "\033[2XOneConjugateSubgroupNotPermutingWith\033[102X", "3.2-11", 
      [ 3, 2, 11 ], 292, 11, "oneconjugatesubgroupnotpermutingwith", 
      "X809E1C8E8384ADE8" ], 
  [ "\033[2XOneConjugateSubgroupNotPermutingWithInParent\033[102X", "3.2-11", 
      [ 3, 2, 11 ], 292, 11, "oneconjugatesubgroupnotpermutingwithinparent", 
      "X809E1C8E8384ADE8" ], 
  [ "\033[2XIsWeaklySPermutable\033[102X", "3.2-12", [ 3, 2, 12 ], 317, 11, 
      "isweaklyspermutable", "X7AC58CFF87770C6C" ], 
  [ "\033[2XIsWeaklySPermutableInParent\033[102X", "3.2-12", [ 3, 2, 12 ], 
      317, 11, "isweaklyspermutableinparent", "X7AC58CFF87770C6C" ], 
  [ "\033[2XOneElementShowingNotWeaklySPermutable\033[102X", "3.2-13", 
      [ 3, 2, 13 ], 326, 12, "oneelementshowingnotweaklyspermutable", 
      "X870923B4798E5097" ], 
  [ "\033[2XOneElementShowingNotWeaklySPermutableInParent\033[102X", 
      "3.2-13", [ 3, 2, 13 ], 326, 12, 
      "oneelementshowingnotweaklyspermutableinparent", "X870923B4798E5097" ], 
  [ "\033[2XIsWeaklyPermutable\033[102X", "3.2-14", [ 3, 2, 14 ], 337, 12, 
      "isweaklypermutable", "X85E85FBF78DAB08E" ], 
  [ "\033[2XIsWeaklyPermutableInParent\033[102X", "3.2-14", [ 3, 2, 14 ], 
      337, 12, "isweaklypermutableinparent", "X85E85FBF78DAB08E" ], 
  [ "\033[2XOneElementShowingNotWeaklyPermutable\033[102X", "3.2-15", 
      [ 3, 2, 15 ], 346, 12, "oneelementshowingnotweaklypermutable", 
      "X8427C8DD78732D56" ], 
  [ "\033[2XOneElementShowingNotWeaklyPermutableInParent\033[102X", "3.2-15", 
      [ 3, 2, 15 ], 346, 12, "oneelementshowingnotweaklypermutableinparent", 
      "X8427C8DD78732D56" ], 
  [ "\033[2XIsWeaklyNormal\033[102X", "3.2-16", [ 3, 2, 16 ], 357, 12, 
      "isweaklynormal", "X84BE89EF8140D2C0" ], 
  [ "\033[2XIsWeaklyNormalInParent\033[102X", "3.2-16", [ 3, 2, 16 ], 357, 
      12, "isweaklynormalinparent", "X84BE89EF8140D2C0" ], 
  [ "\033[2XOneElementShowingNotWeaklyNormal\033[102X", "3.2-17", 
      [ 3, 2, 17 ], 366, 12, "oneelementshowingnotweaklynormal", 
      "X82C8AE027E578ACF" ], 
  [ "\033[2XOneElementShowingNotWeaklyNormalInParent\033[102X", "3.2-17", 
      [ 3, 2, 17 ], 366, 12, "oneelementshowingnotweaklynormalinparent", 
      "X82C8AE027E578ACF" ], 
  [ "\033[2XIsWithSubnormalizerCondition\033[102X", "3.2-18", [ 3, 2, 18 ], 
      392, 13, "iswithsubnormalizercondition", "X872EA72A7CEC3E65" ], 
  [ "\033[2XIsWithSubnormalizerConditionInParent\033[102X", "3.2-18", 
      [ 3, 2, 18 ], 392, 13, "iswithsubnormalizerconditioninparent", 
      "X872EA72A7CEC3E65" ], 
  [ "\033[2XIsWithSubnormaliserCondition\033[102X", "3.2-18", [ 3, 2, 18 ], 
      392, 13, "iswithsubnormalisercondition", "X872EA72A7CEC3E65" ], 
  [ "\033[2XIsWithSubnormaliserConditionInParent\033[102X", "3.2-18", 
      [ 3, 2, 18 ], 392, 13, "iswithsubnormaliserconditioninparent", 
      "X872EA72A7CEC3E65" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotNormal\033[102X", "3.2-19", 
      [ 3, 2, 19 ], 406, 13, "onesubgroupinwhichsubnormalnotnormal", 
      "X7FBEC9DD7C8AED52" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotNormalInParent\033[102X", "3.2-19", 
      [ 3, 2, 19 ], 406, 13, "onesubgroupinwhichsubnormalnotnormalinparent", 
      "X7FBEC9DD7C8AED52" ], 
  [ "\033[2XIsWithSubpermutizerCondition\033[102X", "3.2-20", [ 3, 2, 20 ], 
      414, 13, "iswithsubpermutizercondition", "X87CA542C7E1FEEF3" ], 
  [ "\033[2XIsWithSubpermutizerConditionInParent\033[102X", "3.2-20", 
      [ 3, 2, 20 ], 414, 13, "iswithsubpermutizerconditioninparent", 
      "X87CA542C7E1FEEF3" ], 
  [ "\033[2XIsWithSubpermutiserCondition\033[102X", "3.2-20", [ 3, 2, 20 ], 
      414, 13, "iswithsubpermutisercondition", "X87CA542C7E1FEEF3" ], 
  [ "\033[2XIsWithSubpermutiserConditionInParent\033[102X", "3.2-20", 
      [ 3, 2, 20 ], 414, 13, "iswithsubpermutiserconditioninparent", 
      "X87CA542C7E1FEEF3" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotPermutable\033[102X", "3.2-21", 
      [ 3, 2, 21 ], 428, 13, "onesubgroupinwhichsubnormalnotpermutable", 
      "X79648B4F8758E187" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotPermutableInParent\033[102X", 
      "3.2-21", [ 3, 2, 21 ], 428, 13, 
      "onesubgroupinwhichsubnormalnotpermutableinparent", "X79648B4F8758E187" 
     ], 
  [ "\033[2XIsWithSSubpermutizerCondition\033[102X", "3.2-22", [ 3, 2, 22 ], 
      436, 14, "iswithssubpermutizercondition", "X831F5B8787BB111F" ], 
  [ "\033[2XIsWithSSubpermutizerConditionInParent\033[102X", "3.2-22", 
      [ 3, 2, 22 ], 436, 14, "iswithssubpermutizerconditioninparent", 
      "X831F5B8787BB111F" ], 
  [ "\033[2XIsWithSSubpermutiserCondition\033[102X", "3.2-22", [ 3, 2, 22 ], 
      436, 14, "iswithssubpermutisercondition", "X831F5B8787BB111F" ], 
  [ "\033[2XIsWithSSubpermutiserConditionInParent\033[102X", "3.2-22", 
      [ 3, 2, 22 ], 436, 14, "iswithssubpermutiserconditioninparent", 
      "X831F5B8787BB111F" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotSPermutable\033[102X", "3.2-23", 
      [ 3, 2, 23 ], 450, 14, "onesubgroupinwhichsubnormalnotspermutable", 
      "X7AC9002B7D5AB2DA" ], 
  [ "\033[2XOneSubgroupInWhichSubnormalNotSPermutableInParent\033[102X", 
      "3.2-23", [ 3, 2, 23 ], 450, 14, 
      "onesubgroupinwhichsubnormalnotspermutableinparent", 
      "X7AC9002B7D5AB2DA" ], 
  [ "\033[2XOneSubnormalNonNormalSubgroup\033[102X", "4.1-1", [ 4, 1, 1 ], 
      28, 15, "onesubnormalnonnormalsubgroup", "X7E15C5F778535A28" ], 
  [ "\033[2XOneSubnormalNonPermutableSubgroup\033[102X", "4.1-2", 
      [ 4, 1, 2 ], 55, 16, "onesubnormalnonpermutablesubgroup", 
      "X7F5EE21F85A8D14F" ], 
  [ "\033[2XOneSubnormalNonSPermutableSubgroup\033[102X", "4.1-3", 
      [ 4, 1, 3 ], 87, 16, "onesubnormalnonspermutablesubgroup", 
      "X7D7717657B9C7BEB" ], 
  [ "\033[2XOneSubnormalNonConjugatePermutableSubgroup\033[102X", "4.1-4", 
      [ 4, 1, 4 ], 113, 17, "onesubnormalnonconjugatepermutablesubgroup", 
      "X7878496C869CB90C" ], 
  [ "\033[2XOneSubnormalNonSNPermutableSubgroup\033[102X", "4.1-5", 
      [ 4, 1, 5 ], 137, 17, "onesubnormalnonsnpermutablesubgroup", 
      "X7B23E3857CA178FE" ], 
  [ "\033[2XIsTGroup\033[102X", "4.2-1", [ 4, 2, 1 ], 164, 17, "istgroup", 
      "X7930E5AD817BE4B3" ], 
  [ "\033[2XIsPTGroup\033[102X", "4.2-2", [ 4, 2, 2 ], 201, 18, "isptgroup", 
      "X7CF2634F84EC572B" ], 
  [ "\033[2XIsPSTGroup\033[102X", "4.2-3", [ 4, 2, 3 ], 235, 19, 
      "ispstgroup", "X7BB4D5A782FF5B0E" ], 
  [ "\033[2XIsCPTGroup\033[102X", "4.2-4", [ 4, 2, 4 ], 284, 19, 
      "iscptgroup", "X8789176282320022" ], 
  [ "\033[2XIsPSNTGroup\033[102X", "4.2-5", [ 4, 2, 5 ], 302, 20, 
      "ispsntgroup", "X7B9EBEA07DBE246F" ], 
  [ "\033[2XIsPSupersolvable\033[102X", "5.1-1", [ 5, 1, 1 ], 22, 21, 
      "ispsupersolvable", "X7B9F19A37F4A5B35" ], 
  [ "\033[2XIsPSupersoluble\033[102X", "5.1-1", [ 5, 1, 1 ], 22, 21, 
      "ispsupersoluble", "X7B9F19A37F4A5B35" ], 
  [ "\033[2XIsCp\033[102X", "5.2-1", [ 5, 2, 1 ], 74, 22, "iscp", 
      "X780657F179FFB7EE" ], 
  [ "\033[2XIsXp\033[102X", "5.2-2", [ 5, 2, 2 ], 105, 23, "isxp", 
      "X82953B4878F88327" ], 
  [ "\033[2XIsYp\033[102X", "5.2-3", [ 5, 2, 3 ], 132, 23, "isyp", 
      "X8304885C78E4A584" ], 
  [ "\033[2XIsAbCp\033[102X", "5.3-1", [ 5, 3, 1 ], 167, 24, "isabcp", 
      "X8775CAFD80D3FC02" ], 
  [ "\033[2XIsDedekindSylow\033[102X", "5.3-2", [ 5, 3, 2 ], 190, 24, 
      "isdedekindsylow", "X7A6372D3871E8E55" ], 
  [ "\033[2XIwasawaTripleWithSubgroup\033[102X", "5.3-3", [ 5, 3, 3 ], 220, 
      24, "iwasawatriplewithsubgroup", "X812C3A017F534CC0" ], 
  [ "\033[2XIwasawaTriple\033[102X", "5.3-4", [ 5, 3, 4 ], 251, 25, 
      "iwasawatriple", "X7E86B21086879C48" ], 
  [ "\033[2XIsIwasawaSylow\033[102X", "5.3-5", [ 5, 3, 5 ], 298, 26, 
      "isiwasawasylow", "X8121A92F7EABEA0C" ], 
  [ "\033[2XAreMutuallyPermutableSubgroups\033[102X", "6.1-1", [ 6, 1, 1 ], 
      21, 27, "aremutuallypermutablesubgroups", "X876F4E0D7C796134" ], 
  [ "\033[2XOnePairShowingNotMutuallyPermutableSubgroups\033[102X", "6.1-2", 
      [ 6, 1, 2 ], 33, 27, "onepairshowingnotmutuallypermutablesubgroups", 
      "X80225ABC79C7875F" ], 
  [ "\033[2XAreTotallyPermutableSubgroups\033[102X", "6.1-3", [ 6, 1, 3 ], 
      42, 28, "aretotallypermutablesubgroups", "X7D58DFE57AA4573B" ], 
  [ "\033[2XOnePairShowingNotTotallyPermutableSubgroups\033[102X", "6.1-4", 
      [ 6, 1, 4 ], 53, 28, "onepairshowingnottotallypermutablesubgroups", 
      "X7B51474D878ACD11" ], 
  [ "\033[2XAreMutuallyFPermutableSubgroups\033[102X", "6.1-5", [ 6, 1, 5 ], 
      92, 28, "aremutuallyfpermutablesubgroups", "X823C6D68813B3AC8" ], 
  [ "\033[2XOnePairShowingNotMutuallyFPermutableSubgroups\033[102X", "6.1-6", 
      [ 6, 1, 6 ], 103, 29, "onepairshowingnotmutuallyfpermutablesubgroups", 
      "X83E0517A800AB839" ], 
  [ "\033[2XAreTotallyFPermutableSubgroups\033[102X", "6.1-7", [ 6, 1, 7 ], 
      116, 29, "aretotallyfpermutablesubgroups", "X7B9DA1C2834CA53D" ], 
  [ "\033[2XOnePairShowingNotTotallyFPermutableSubgroups\033[102X", "6.1-8", 
      [ 6, 1, 8 ], 128, 29, "onepairshowingnottotallyfpermutablesubgroups", 
      "X7CD0B5737A25C1AD" ], 
  [ "\033[2XAllSubnormalSubgroups\033[102X", "7.1-1", [ 7, 1, 1 ], 11, 30, 
      "allsubnormalsubgroups", "X81EA23787BCD8633" ], 
  [ "\033[2XPrimesDividingSize\033[102X", "7.1-2", [ 7, 1, 2 ], 31, 30, 
      "primesdividingsize", "X858C07DA815A2E9A" ], 
  [ "\033[2XSylowSubgroups\033[102X", "7.1-3", [ 7, 1, 3 ], 45, 31, 
      "sylowsubgroups", "X7B07AAD37F7CEDEB" ], 
  [ "\033[2XIsSCGroup\033[102X", "7.1-4", [ 7, 1, 4 ], 67, 31, "isscgroup", 
      "X7E01D1C47814DA3C" ], 
  [ "\033[2XIsSylowTowerGroup\033[102X", "7.1-5", [ 7, 1, 5 ], 92, 31, 
      "issylowtowergroup", "X798736C17DD23F8A" ], 
  [ "\033[2XPermutizer\033[102X", "7.1-6", [ 7, 1, 6 ], 110, 32, 
      "permutizer", "X81FCDD7C7A5D1658" ], 
  [ "\033[2XPermutiser\033[102X", "7.1-6", [ 7, 1, 6 ], 110, 32, 
      "permutiser", "X81FCDD7C7A5D1658" ], 
  [ "\033[2XAllGeneratorsCyclicPGroup\033[102X", "7.1-7", [ 7, 1, 7 ], 128, 
      32, "allgeneratorscyclicpgroup", "X7D47DF77826C1BE0" ] ]
);
