> < ^ Date: Wed, 29 Jan 1997 09:19:56 +0100
> ^ From: Peter F. Blanchard <pfb3h@weyl.math.virginia.edu >
> ^ Subject: AutGroupSagGroup (forwarded)

This mail was not originally accepted by 'Miles' because of technical
problems:

Dear Mr. and Mrs. Forum,
I have been using Micheal Smith's Automorphism Group share
package quite a bit lately. It is a wonderful and welcome replacement for
a rickety old backtrack program I had been using. Much thanks to Micheal.
Here is my question: can someone tell me how to multiply cosets
of subgroups of automorphism groups? It seems that this was left out, but
it is probably not difficult to do. An example follows which illustrates
how the problem comes up when trying to calculate an intersection of
subgroups of an automorphism group.

```--

Peter Blanchard                     http://vega.math.ualberta.ca/~pblancha
Dept. of Mathematical Sciences      e-mail: pblancha@vega.math.ualberta.ca
University of Alberta               "Every day holds a wonder that's got
to be seen, baby." ------- Carol King
```

Example:

```gap> grp := SpecialAgGroup(DihedralGroup(AgWords,8));
Group( s, d1, d2 )
gap> autgrp := AutGroupSagGroup(grp);
Group( Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]), InnerAut(Group( s, d1,
d2 ), d1), InnerAut(Group( s, d1, d2 ), s) )
gap> t1 := Subgroup(autgrp,[autgrp.1]);
Subgroup( Group( Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]), InnerAut(Group(
s, d1, d2 ), d1), InnerAut(Group( s, d1, d2 ), s) ),
[ Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]) ] )
gap> t2 := Subgroup(autgrp,[autgrp.2]);
Subgroup( Group( Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]), InnerAut(Group(
s, d1, d2 ), d1), InnerAut(Group( s, d1, d2 ), s) ),
[ InnerAut(Group( s, d1, d2 ), d1) ] )
gap> Intersection(t1,t2);
Error, product of <a> and <b> is not defined in
<rec1> * <rec2> called from
arg[1].operations.Stabilizer( arg[1], arg[2], arg[3] ) called from
Stabilizer( H, Coset( G ), OnRight ) called from
D.operations.Intersection( I, D ) called from
Intersection( t1, t2 ) called from
main loop
brk> a;
(Subgroup( Group( Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]), InnerAut(Group(
s, d1, d2 ), d1), InnerAut(Group( s, d1, d2 ), s) ),
[ Aut(Group( s, d1, d2 ), [ s*d1, d1, d2 ]) ] )*InnerAut(Group( s, d1,
d2 ), IdAgWord))
brk> b;
InnerAut(Group( s, d1, d2 ), d1)
brk> quit;
gap> LogTo();
```

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