[GAP Forum] IsMinimalNonmonomial(AlternatingGroup(5));

[Thomas Breuer]

Dear Bill,

thanks for your message.

Yes, currently there is no 'IsMinimalNonmonomial' method for nonsolvable
groups in the GAP library.
When I wrote the code for solvable minimal nonmonomial groups (about
thirty years ago), I was interested in van der Waall's classification of
solvable minimal nonmonomial groups; I did not think about asking the
question for nonsolvable groups.

I see the following ways to improve the situation.

- Implement a mehod for nonsolvable groups.
  (Just providing some simpleminded code just in order to get an answer
  instead of a "no method found" error message is not a good idea.
  If someone is really interested in the question for nonsolvable groups
  then probably the first step is to ask for minimal nonsolvable simple
  groups, and then one looks at the monomiality condition for the subgroups
  of these groups.)

- Change the documentation such that it says that GAP can currently answer
  this question only for solvable groups.
  (An example for such a solution is the function 'Omega',
  which states: @At the moment methods exist only for abelian G and n=1.@
  Note that this statement is not correct.)

- Give a more informative error message if the argument is a nonsolvable
  group.
  (Again, 'Omega' is an example where this happens.)

All the best,
Thomas


On Sun, May 02, 2021 at 12:21:57AM +0200, Bill Allombert wrote:
> Dear Forum,
> 
> I found
> 
> gap> IsMinimalNonmonomial(AlternatingGroup(5));
> Error, no method found! For debugging hints type ?Recovery from
> NoMethodFound
> Error, no 3rd choice method found for `IsMinimalNonmonomial' on 1
> arguments at /usr/share/gap/lib/methsel2.g:249 called from
> 
> Is it expected ?
> 
> I found this while doing:
> gap> AllGroups(Size,[1..100],IsMinimalNonmonomial,true);
> Error, no method found! For debugging hints type ?Recovery from
> 
> Cheers,
> Bill.