Dear Forum,

Chris Charnes wrote:

Dear Forum, I have noticed the following problem in version 3.3
with the Automorphisms function.

gap> c;
Group( ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13) )

gap> Automorphisms(c);
Error, Variable: 'Automorphisms' must have a value

It's not really a bug, but it might be necessary to upgrade your
installation. Some comments:

`Automorphisms' is not provided by the GAP library but by the share package
`Sisyphos'. Thus one has to load this package to get access to this
function:

gap> RequirePackage("sisyphos");
#I LoadPackage tries "/usd/gap/3.4/pkg/sisyphos/init.g"

(If you are in doubt whether a function requires a share library look it up
in the help function. The header line indicates the chapter name at the
right).

gap> g:=Group((1,2,3,4,5,6,7,8,9,10,11,12,13));;

The function `Automorphisms' however requires the group to be an AgGroup,
so one has to convert it.

gap> a:=AgGroup(g);

The function `Automorphisms' calls the external `Sisyphos' binary. This
implies that this share library has to be installed. The installation
involves compilation. The share package is called by `Exec' which works only
on Unix-based systems.

gap> au:=Automorphisms(a);
#I  ReadPkg( "/usd/gap/3.4/pkg/sisyphos/gap/sisgroup.g" )
#I  ExecPkg: executing cd .; /usd/gap/3.4/pkg/sisyphos/bin/sis -b -q -s gap  -\
t 200000 -m 66666 </var/tmp/tmp.014111 >/var/tmp/tmp.a14111
#I  Read( "/var/tmp/tmp.a14111" )
#I  Read( "/var/tmp/tmp.a14111" ) done
rec(
sizeAutG := 12,
sizeInnG := 1,
sizeOutG := 12,
generators :=
[ GroupHomomorphismByImages( Group( g ), Group( g ), [ g ], [ g^2 ] ) ] )

If you are willing to install the latest version (3.4, patchlevel 2) --
this is recommended anyhow because it fixes several bugs -- you can also use
the function `AutomorphismGroup' which also works for permutation groups.

gap> AutomorphismGroup(g);
Group( GroupHomomorphismByImages( Group( ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,
13) ), Group( ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13) ),
[ ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13) ],
[ ( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12) ] ) )

It works likewise for AgGroups:
gap> AutomorphismGroup(a);
Group( GroupHomomorphismByImages( Group( g ), Group( g ), [ g ], [ g^2 ] ) )

However you should note, that `AutomorphismGroup' is a general purpose
routine which in general runs much slower for p-groups than `Automorphisms'.
On the other hand it does not require the group to be a p-Group.

Best regards,

Alexander Hulpke