[GAP Forum] IsConjugate() after CharacterTableDirectProduct()

[Alexander Hulpke]

Dear GAP Forum,

Kuersat Aker wrote:

> Inside my GAP code,
> a function call to IsConjugate() before and after
> a function call to CharacterTableDirectProduct() behaves very differently.
> 
> The first call at (1) works fine, returns false, which is the expected result.
> 
> After a call to CharacterTableDirectProduct(), the second call to IsConjugate() at (2) ends up in a brk>.

What is happening is that you are working with a finitely presented group. For calculations in known finite groups this is a very inefficient representation and less functionality is available, as for other representations.
> Or is there a bug?
This is not a bug -- GAP simply has reached the end of its capabilities for finitely presented groups.
The calculation of the character table detects that the group is solvable. A subsequent conjugacy test now is trying to use a method for solvable groups, this fails as GAp is not aware of a method to compute a p-central series for finitely presented groups.
> Is there a way around this problem?

In this particular case it is relatiuvely easy to tell GAP that it can use existing routines for the PCentral series also for the groups in question, by issuing the following two commands:

InstallOtherMethod( PcgsCentralSeries, "for pcgs computable use SpecialPcgs",
 true,[CanEasilyComputePcgs],0,DoCentralSeriesPcgsIfNilpot);

InstallOtherMethod( PcgsPCentralSeriesPGroup,
 "for pcgs computable use SpecialPcgs",
 true,[CanEasilyComputePcgs],0,DoCentralSeriesPcgsIfNilpot);

However using the representation as finitely presented group is very inefficient and prone to run into other issues of missing methods. It will be much better to represent your groups (as they are known to be solvable) as PCgroups, for example using the command IsomorphismPcGroup.

Best,

    Alexander Hulpke




-- Colorado State University, Department of Mathematics,
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