[GAP Forum] to get correction in code.

[Harsha Arora]

Dear Sir

I have written code to get autocenter of a group , that is collection of
all those elements in G which are fixed by all automorphisms of G, like
center of G as centeral elements are fixed by all inner automorphisms of G
. I have got the output. But i m not getting the structure description of
the subgroup. I am getting the message no method is installed.   I also
want to know the way to feed  a group with generators and relation.

Autocenter:=function(G)

local aut,auts,L;

aut:=AutomorphismGroup(G);

L:=Filtered(AsList(G),g->ForAll(AsList(aut), auts->Image(auts,g)=g));

return(L);

end;


function( G ) ... end

Autocenter(CyclicGroup(4));

Error, no method found! For debugging hints type ?Recovery from
NoMethodFound

Error, no 1st choice method found for `AsList' on 2 arguments

Autocenter(CyclicGroup(4));

[ <identity> of ..., f2 ]

StructureDescription(Autocenter(CyclicGroup(4)));

Error, no method found! For debugging hints type ?Recovery from
NoMethodFound

Error, no 1st choice method found for `StructureDescription' on 1 arguments

IsSubgroup(CyclicGroup(4),Autocenter(CyclicGroup(4)));

false
 ALTERNATIVE  WAY IS

image:=function(G,g)

local L,aut,auts,i,j;

aut:=AutomorphismGroup(G);

L:=[];

for auts in aut do

AddSet(L, Image(auts,g));od;

return(L);

end;

function( G, g ) ... end

autc:=function(G)

local H;

H:=Filtered(G, g->Size(image(G,g)=1));

return(H);

end;

function( G ) ... end

autc(CyclicGroup(4));

Error, no method found! For debugging hints type ?Recovery from
NoMethodFound

Error, no 1st choice method found for `Size' on 1 arguments.


PLEASE SOLVE MY PROBLEM.

With regards
Harsha
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