GAP: Arbeitsweise

RecFields

  gap> RecFields(cube);
  [ "isDomain", "isGroup", "identity", "generators", "operations",
    "isPermGroup", "isFinite", "1", "2", "3", "4", "5", "6" ]

  gap> Size(cube);
  43252003274489856000

  gap> RecFields(cube);
  [ "isDomain", "isGroup", "identity", "generators", "operations",
    "isPermGroup", "isFinite", "1", "2", "3", "4", "5", "6", "orbit",
    "transversal", "stabilizer", "isParent", "stabChainOptions", "stabChain",
    "size" ]

• orbit
• transversal
• stabilizer, stabCainOptions, stabChain
• size

• SylowSubgroups
• Centralizer
• DerivedSubgroup
• FittingSubgroup
• FrattiniSubgroup

  gap> y2:=SylowSubgroup(cube, 11);

  Subgroup( Group( ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)
  (11,35,27,19), ( 1,17,41,40)( 4,20,44,37)( 6,22,46,35)( 9,11,16,14)
  (10,13,15,12), ( 6,25,43,16)( 7,28,42,13)( 8,30,41,11)(17,19,24,22)
  (18,21,23,20), ( 3,38,43,19)( 5,36,45,21)( 8,33,48,24)(25,27,32,30)
  (26,29,31,28), ( 1,14,48,27)( 2,12,47,29)( 3, 9,46,32)(33,35,40,38)
  (34,37,39,36), (14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)
  (42,45,47,44) ),
  [ ( 4,26,20,28,37,29, 7,44,31,23,47)( 5,13,21,12,36,18,15,45,42,39,10) ] )

  gap> Centre(cube);
  Subgroup( Group( ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)
  (11,35,27,19), ( 1,17,41,40)( 4,20,44,37)( 6,22,46,35)( 9,11,16,14)
  (10,13,15,12), ( 6,25,43,16)( 7,28,42,13)( 8,30,41,11)(17,19,24,22)
  (18,21,23,20), ( 3,38,43,19)( 5,36,45,21)( 8,33,48,24)(25,27,32,30)
  (26,29,31,28), ( 1,14,48,27)( 2,12,47,29)( 3, 9,46,32)(33,35,40,38)
  (34,37,39,36), (14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)
  (42,45,47,44) ),
  [ ( 2,34)( 4,10)( 5,26)( 7,18)(12,37)(13,20)(15,44)(21,28)(23,42)(29,36)
    (31,45)(39,47) ] )

  gap> RecFields(cube);
  [ "isDomain", "isGroup", "identity", "generators", "operations",
    "isPermGroup", "isFinite", "1", "2", "3", "4", "5", "6", "orbit",
    "transversal", "stabilizer", "isParent", "stabChainOptions", "stabChain",
    "size", "sylowSubgroups", "isTrivial", "centre" ]

  gap> RecFields(cube);
  [ "isDomain", "isGroup", "identity", "generators", "operations",
    "isPermGroup", "isFinite", "1", "2", "3", "4", "5", "6", "orbit",
    "transversal", "stabilizer", "isParent", "stabChainOptions", "stabChain",
    "size", "sylowSubgroups", "isTrivial", "centre", "trivialSubgroup",
    "derivedSubgroup", "pCores", "lowerCentralSeries", "isNilpotent",
    "isSolvable", "compositionSeries", "isSimple", "radical" ]

Bibliotheken

• Algorithmen: lib/group.g
• Gruppen: grp/basic.grp

  gap> c13:=CyclicGroup(11);
  Group( ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11) )

  gap> s8:=SymmetricGroup(8);
  Group( (1,8), (2,8), (3,8), (4,8), (5,8), (6,8), (7,8) )

  gap> g:=PrimitiveGroup(12,3);
  M(11)

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