[GAP Forum] some questions

[R. Keith Dennis]

Dear Jack,

thanks very much for this note, as well as your earlier note.

Just what I needed!


> Here are some hopefully helpful suggestions from Alexander Konovalov, 
> Steve Linton, and myself.

> > 2.  How does one trap errors?  E.g., something like
> > 
> > if defined NumberSmallgroups(n) then
> >    Print(.....);
> >  else	
> >    Print("NumberSmallGroups(",n,") is not defined\n");
> > fi;
>
> There is no method in GAP to trap errors, but the list of orders covered 
> by the small groups library is at:

I realize that GAP is extremely useful for interactive programming,
and 'break'ing upon errors helps to detect & fix problems, but not
being able to gracefully exit from a computation and continue on to
the next case, makes things a bit difficult, but perhaps mainly for
those not so familiar with what might go wrong.

>    http://www.tu-bs.de:8080/~hubesche/small.html
>
> If you would like, we would be happy to forward you this list as a 
> simple GAP function that returns true/false based on whether an integer 
> falls into one of these categories.

Thanks for the offer, but that's not necessary.  I had hoped for a
general solution that I presumed I had missed in the documentation.

If there were a way to add such a feature to GAP it seems to me that
it would be extremely valuable.

I'm too accustomed to programming in perl where I protect myself
(most of the time) by "if defined ... then".

A related question:  If one has defined a function of 2 or 3 or
whatever variables of a certain type, is there a way to program in
returning usage if no (or the wrong number, or type) entries are
given?  I write too many functions & it would be much more convenient
if they would remind me as to what they do & what correct input should
be, especially when I give them the wrong number of entries, or the
wrong type.

> > 4.  Is there any reason SubdirectProduct is called that instead of
> > PullBack?  It seems to me the name is wrong or at least misleading.  I

> The definition in GAP corresponds to its main use in the construction of 
> small perfect groups.  This definition is equivalent to the standard 
> definition for subdirect products of pairs of groups by Lemma 2.1.2.iii 

I can't seem to find my copy of the book at the moment, but it just
struck me as strange terminology as, for example, direct product was
not a special case.

> of Holt&Plesken's book, "Perfect Groups."  As noted in section 2.1.3 of 
> this book, the general case does not have an easy translation into this 

Exactly.  I guess that was my point.

> pullback framework, but within GAP one can only form subdirect products 
> of two groups, so this issue does not arise.

> Please do not hesitate to ask more questions! You can write to GAP Forum
> with questions that you believe are of general interest, and to GAP
> Support (support at gap-system.org) with more technical questions.

Thanks!

Another simple one then:  Is there a simple way to get the lattice
of normal subgroups of a group?  One can get the lattice of all
subgroups, and the collection of normal subgroups, but I didn't
see a SubLattice command nor could I find a way to filter.  I presume
there is a way.  And the same question for the subnormal subgroups.

Thanks again for your help!

Keith