1.2 GroupPresentationGPL

GroupPresentationGPL( grname, number )

GroupPresentationGPL returns a record containing the presentation with number number of the group with name grname. grname is expected to be a string.

    gap> mcl := GroupPresentationGPL( "McL", 1);
    GroupPresentationGPL( "McL", 1 )

This record contains the following components:

.name contains a descriptive name for the underlying group.

   gap> mcl.name;
   "McL"

.number is the same as the number number above.

   gap> mcl.number;
   1

.stringPresentation contains presentation number number of group name in string format. The string presentation is a list of maximal four entries. If all four entries are bound they will have the following contents:

1. A string representing a Coxeter graph.
2. A string representing generators that are not introduced by the Coxeter graph.
3. A string representing relators, necessary for the definition of the presentation.
4. A string representing relators, not necessary for the definition of the presentation, but helpful for a coset enumeration process.

It is not required that all entries are bound, but at least one of the entries 1 or 2 should be. It is important that an entry is on that position of the string presentation list as is indicated by the scheme above. Refer to chapter 2 for information on the formats required for the mentioned strings.

   gap> mcl.stringPresentation;
   [ "a3b5c3d3f6e,a4e3c4f",, "a=(cf)^2,b=(ef)^3,(eab)^3,(bce)^5,(aecd)^4,
     (cef)^7", "(bcd)^5" ]

.subgroups when present, contains a list of strings defining subgroups of the group in the given presentation. The first entry contains a descriptive name of the subgroup. The names correspond with the names used by GAP to identify character tables as much as possible. The second entry consist of a string representing words, generating the subgroup. The third entry is of the form "_A**". This string indicates the source of the words. ( A stands for Author, see the source file for definitions of the used abbrevations for names of authors. ) The existence of a string "_MT" ( resp. "_MF" ) indicates that the subgroup is maximal ( resp. non-maximal ). Eventually, some other common names for the subgroup are added.

  gap> mcl.subgroups;
  [ [ "U4(3)", "cef,dfcd", "_APS", "_MT" ], 
   [ "M22", "a,b,c,d,e", "_APS", "_MT" ], 
   [ "U3(5)", "b,(de)^(cbac),acdcbeace,(cdfbeaecd)^3", "_APS", "_MT" ], 
   [ "3^{1+4}_+:2.S5", "cdfbeaecd,cbadecbcbadcecbaecd", "_APS", "_MT" ] ]

.text describes the source of the presentation.

   gap> mcl.text;
   "origin: Low Rank Representations and Graphs for Sporadic Groups"

.operations contains a function that takes care of the output to the screen when GroupPresentationGPL is called.