Let me answer your questions:
> Subject: products
> I'm a very new user of GAP and try to run it on 486.
> 1) If H and K are two subgroups of G, what is the easiest way of
> computing their product HK as a subgroup of G?
> 2) Does it exist some kind of tutorial for the beginner?
> Thanks a lot,
> Thierry Dana-Picard.
ad 1): Usually the notation HK for two subgroups H and K is used to
mean the *set* of all elements hk with h in H and k in K. This is a
subgroup only if HK = KH. If this is the case, then the command
Closure(H,K) will compute this *subgroup* HK, as described in section
7.17 (pages 227/8) of the manual. If HK is *not* a subgroup ( as would
alredy happen if you take two cyclic subgroups of order 2 in the
symmetric group of degree 3) then there is *no* GAP command to compute
this set, you would have to create this *set* by a little self-written
ad 2): There is no special tutorial for GAP, however chapter 1 of the
manual, called "About GAP" (pages 37 -150) provides an easy
introduction to GAP. Further you may be interested that a Summer
School on Computational Group Theory using GAP as the main vehicle is
planned as part of the 'Groups 1993, Galway/St.Andrews' meeting to be
held in Galway, Ireland, August 1 to 14.