# why can not define G := Group((1),(3,2));;

gap> G := Group((1),(3,2));;
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) called from
<function "Group">( <arguments> )
called from read-eval loop at line 6 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue


before finding character table of permutation group S3 - 1,3,2

got error in above command

• you could always try asking on stackoverflow.com – raindrop Jul 28 '13 at 2:21
• Are the users who downvoted and voted to close familiar with the software GAP? I don't understand the question so I cannot personally see one way or the other about whether or not this deserves downvotes or close votes. I expect if it deserved them there should be some explanation as to why in the comments, as well as efforts to engage with the OP, but I see none. – anon Jul 28 '13 at 8:29
• The question is about the meaning of the error message in GAP, though it suffers from inconsistent notation and could be formulated better. I think it's fine to ask it here - the gap-system tag at stackoverflow.com seems much less attended. Try to debug your input and see how GAP parses (1) and (3,2) - you will see the difference which should give you a hint. – Alexander Konovalov Jul 28 '13 at 11:42
• @scaaahu: Please don't make such conclusions just reading the GAP Forum: it is entirely plausible that the OP wrote to GAP Support, which is not a public mailing list, but did not get a quick reply from there and decided to repeat the question here. – Alexander Konovalov Jul 28 '13 at 20:11
• @scaaahu Indeed, I've assumed you are subscribed to the Forum or looked at the GAP Forum Archive, not that you'd like the OP to say this explicitly in the post. – Alexander Konovalov Jul 29 '13 at 9:54

Now after the question is no longer on hold, I can reply with more details:

1) The error about the wrong usage of Group usually means that the group can not be generated by the arguments. For example,

gap> Group(1);
#I  no groups of cyclotomics allowed because of incompatible ^
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) called from
<function "Group">( <arguments> )


2) What's then wrong with the arguments in the question? See how GAP evaluates various inputs:

gap> (3,2); # works OK
(2,3)
gap> ();    # this is the notation for the identity permutation
()
gap> (1);   # this is an integer one in brackets
1


Thus, Group((1),(3,2)) tries to generate a group with an integer 1 and a permutation (3,2) as generators, what obviously does not make sense

3) What does (1) in the original question actually mean? If this has to be an identity permutation, one should use () - however, there is no need to add the identity element of the group to the list of generators, so Group((3,2)) just suffices:

gap> Group((3,2));
Group([ (2,3) ])


4) This may be not the intended group, however, since the question contains "permutation group S3 - 1,3,2" - it's unclear what is the meaning of "1,3,2" here, but if the intention was to create a symmetric group of permutations of degree 3, here there are several ways to achieve this:

gap> Group((1,2),(1,2,3));
Group([ (1,2), (1,2,3) ])
gap> SymmetricGroup(3);
Sym( [ 1 .. 3 ] )


5) Finally, the following hint about character tables may be useful:

One can compute the character table "on-fly" for a given group, and if some methods depend on random states, the result may differ each time you call CharacterTable (conjugacy classes may be ordered in a different way). For groups whose character tables are available from The GAP Character Table Library, the table will be retrieved from the library so the result will be the same each time. Compare Display(CharacterTable(SymmetricGroup(3))); and Display(CharacterTable("S3")); to see the difference.

• in another question, i can use wrong notation, it work, math.stackexchange.com/questions/453392/… – Series group Jul 29 '13 at 12:42
• @Seriesgroup: sorry, I do not understand what do you mean in your recent comment. The question linked there is still the same as yesterday. – Alexander Konovalov Jul 29 '13 at 12:47
• @AlexanderKonovalov: May I ask you to take a look at mu question here stackoverflow.com/q/18043036/1842737. Sorry and forgive me for this asking Prof. :) – mrs Aug 4 '13 at 12:48