[GAP Forum] a third output for IsAbelian

[Alexander Hulpke]

Dear Forum,


> On Jan 21, 2015, at 1/21/15 6:32, Ali <alireza_abdollahi at yahoo.com> wrote:
> 
> Dears,
> 
> I have a long list L of groups with finite presentations. I would like to apply IsAbelian on L and Filtered all groups which are not Abelian. Through the computations, IsAbelian could not treat an special group and so the Filtered will not be terminated. I would like to know if there is a way to define a third output for IsAbelian such as FAIL which means that it is tried to test abelianness by a certain limit ( e.g. Time or number of cosets or ...) but not succeeded.  If such thing exists I can apply this new IsAbelian to the list L to obtain all groups which are not abelian or the old IsAbelian fails to give a true or false. Then I can handle the filtered list by hand since I guess the latter list should be short.
> 
> The same question for IsSolvable and ....

This depends a bit on the groups in question, but `IsAbelian' etc. will by default calculate a faithful representation. If your groups are huge this will most likely fail every time.

What I would do as a first step is to look at quotient groups: Solvable Quotient, Action on cosets of Low Index subgroups and see whether rthese quotient groups already exclude the properties. This has (quotient size/subgroup index) easy parameters that will limit the initial calculations.
This should give you a good initial filtering of non-candidates.

Best,

  Alexander Hulpke

> 
> Best Wishes
> Alireza Abdollahi
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