> < ^ From:

< ^ Subject:

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

function.

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.

Joachim Neubueser

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