On Sun, May 31, 2015 at 04:48:59PM +0800, 杨高 wrote:
Do you work with GAP3?
Is it really necessary for you?
>
> Is this the correct and most concise way to construct PGL(2,3) with GAP?
In GAP4 you can just do
gap> ProjectiveGeneralLinearGroup(2,3);
Group([ (3,4), (1,2,4) ])
>
>
> > W:=GeneralLinearGroup(2,3);;
> > H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);;
> > B:=W/H;;
>
>
> Morevoer, I want to construct the character table of this group. But there is
> ian error.
>
>
> >Display(CharTable(B));
> Error, sorry, I don't know how to construct the table of <grp>
> in
> CharTable( B ) called from
> main loop
well, GAP4 has no difficulty here:
gap> H:=Subgroup(W,[[[Z(3),0*Z(3)],[0*Z(3),Z(3)]]]);;
gap> B:=W/H;;
gap> Display(CharacterTable(B));
CT2
2 3 2 . 3 2
3 1 . 1 . .
1a 2a 3a 2b 4a
2P 1a 1a 3a 1a 2b
3P 1a 2a 1a 2b 4a
X.1 1 1 1 1 1
X.2 1 -1 1 1 -1
X.3 2 . -1 2 .
X.4 3 -1 . -1 1
X.5 3 1 . -1 -1
gap>
> So there are question I would like to ask. For constructing character tables,
> what kind of groups can GAP deal with? Can GAP construct the character table
> of PGL(n,m)? If the answer is yes, then how can I do this with it?
You can contruct the character table of a given group, but it gets slower as
the
size etc grows. How far do you need to go with n and m?
There are some infinite families of groups for which GAP can construct
character tables directly,
see
http://www.gap-system.org/Manuals/pkg/ctbllib/doc/chap4.html#X81E3F9A384365282
E.g. for n=2 one can have tables of the PSL groups.
HTH,
Dmitrii
>
>
> Thanks to everyone.
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