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> ^ Subject:

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

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