We are initiating ourselves in the use of GAP. The following question arises
in looking at what GAP does to permutation groups.
It looks like if the man-page is not fully clear on this neither.

When one looks at the output of
gp.stabilizer
if gp is a well defined permutation group, than one finds a record containing
many "transversals". How should these transversals be understood? E.g. they contain
often many "extra comma's".

As an example consider the following output:

Group( (1,2,3,4)(5,6,7,8), (1,2,3), (1,3,5), (1,2)(3,4,7) )
gp.transversal := [ (), (1,2)(3,4,7), (1,2,3), (1,2,3,4)(5,6,7,8), (1,3,5), (1,2,3,4)(5,6,7,8),
  (1,2)(3,4,7), (1,2,3,4)(5,6,7,8) ]
gp.stabilizer :=
rec(
  identity := (),
  generators := [ (2,4,3,5,7)(6,8), (3,5,7), (2,6,7) ],
  orbit := [ 2, 7, 5, 3, 4, 6, 8 ],
  transversal :=
   [ , (), (2,4,3,5,7)(6,8), (2,4,3,5,7)(6,8), (2,4,3,5,7)(6,8), (2,6,7),
      (2,4,3,5,7)(6,8), (2,4,3,5,7)(6,8) ],
  stabilizer := rec(
      identity := (),
      generators := [ (6,8), (3,5,7), (3,4,5), (5,8,7) ],
      orbit := [ 3, 7, 5, 4, 8, 6 ],
      transversal := [ ,, (), (3,4,5), (3,5,7), (6,8), (3,5,7), (5,8,7) ],
      stabilizer := rec(
          identity := (),
          generators := [ (6,8), (4,5,7), (5,8,7) ],
          orbit := [ 4, 7, 5, 8, 6 ],
          transversal := [ ,,, (), (4,5,7), (6,8), (4,5,7), (5,8,7) ],
          stabilizer := rec(
              identity := (),
              generators := [ (6,8), (5,8,7) ],
              orbit := [ 5, 7, 8, 6 ],
              transversal := [ ,,,, (), (6,8), (5,8,7), (5,8,7) ],
              stabilizer := rec(
                  identity := (),
                  generators := [ (6,8), (6,7,8) ],
                  orbit := [ 6, 8, 7 ],
                  transversal := [ ,,,,, (), (6,7,8), (6,8) ],
                  stabilizer := rec(
                      identity := (),
                      generators := [ (7,8) ],
                      orbit := [ 7, 8 ],
                      transversal := [ ,,,,,, (), (7,8) ],
                      stabilizer := rec(
                          identity := (),
                          generators := [  ] ) ) ) ) ) ) )

Thanks a lot.

Is there a procedure in GAP to solve the "word"-problem for permutation groups?
E.g. something like "wordsolve(element, group, group.generators)" ?

Paul Igodt