[GAP Forum] Possible bug with MinimalGeneratingSet()???

[Greg Tener]

Thanks Joe, your reply was very helpful, I can just use
"SmallGeneratingSet" when "MinimalGeneratingSet" fails.

Also, I have a question about terminology/semantics, I thought
"MinimalGeneratingSet" was providing a set of generators such that no
subset of them generates the entire group. Is it, on the contrary,
returning a group with the fewest possible number of generators? (I
was under the impression this would be called a
"MinimumGeneratingSet").

On Sun, Jun 6, 2010 at 8:06 PM, Joe Bohanon <jbohanon2 at gmail.com> wrote:
> Greg and Forum
>
> You might find this link particularly helpful here:
>
> http://mail.gap-system.org/pipermail/forum/2005/001109.html
>
> For non-solvable groups, you can (sort of) get what you want with
> "SmallGeneratingSet".  I would guess from the name that it's not necessarily
> "Minimal", however, it can be very useful if you define a non-solvable
> group, then try (for instance) asking for the center, and you get a subgroup
> with 2 elements and 35 generators (I swear, I've seen that happen before).
> In my experience, it does very well with permutation groups.  With groups
> you define yourself via generators and relations, anything goes.
>
> Joe
>
> On Sun, Jun 6, 2010 at 10:15 PM, Greg Tener <greg.d.tener at gmail.com> wrote:
>>
>> Dear GAP-forum,
>>
>> There might be a problem with MinimalGeneratingSet().  It seems not to
>> work for a particular group, as shown in the following console
>> session:
>>
>> """
>> gap> g := Group( [ (1,2,3,4,5), (1,2,3) ] );
>> Group([ (1,2,3,4,5), (1,2,3) ])
>> gap> MinimalGeneratingSet(g);
>> Error, no method found! For debugging hints type ?Recovery from
>> NoMethodFound
>> Error, no 2nd choice method found for
>> `IndependentGeneratorsOfAbelianGroup' on 1 arguments called from
>> IndependentGeneratorsOfAbelianGroup( G ) called from
>> <function>( <arguments> ) called from read-eval-loop
>> Entering break read-eval-print loop ...
>> you can 'quit;' to quit to outer loop, or
>> you can 'return;' to continue
>> """
>>
>> Am I doing something wrong or could this be a bug? I know nothing
>> about the internals of GAP so I cannot think why this would happen or
>> how to fix it.
>>
>> Thanks,
>> -Greg Tener-
>>
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>
>