[GAP Forum] Urgently Seeking for Help in Calculating the Abelian Invariants of a Group with GAP

[Minghui Liu]

Dear Sir/Madam,

I am a beginner of GAP and would like to use this program to determine the
structure of some groups. Here is the group I am interested in :

Let K_3 be the group generated by three elements a, b, c subject to the
relation that every simple commutator with repeated generators is equal to
1. (For example, [[[a, c], b], c] = 1.) Now let A_3 be the subgroup of K_3
generated by abc, [a, b][b, c][a, c], [[a, b], c] and [[a, c], b] and I
would like to determine the structure of abelianization of A_3. Here is my
code:

F3:=FreeGroup("a","b","c");
B3:=[Comm(Comm(F3.1,F3.2),F3.1),Comm(Comm(F3.1,F3.2),F3.2),Comm(Comm(F3.2,F3.3),F3.2),Comm(Comm(F3.2,F3.3),F3.3),Comm(Comm(F3.1,F3.3),F3.1),Comm(Comm(F3.1,F3.3),F3.3),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.1),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.1),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.1),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.1),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.1),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.1),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.2),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.2),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.2),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.2),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.2),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.2),Comm(Comm(Comm(F3.1,F3.2),F3.3),F3.3),Comm(Comm(Comm(F3.1,F3.3),F3.2),F3.3),Comm(Comm(Comm(F3.2,F3.1),F3.3),F3.3),Comm(Comm(Comm(F3.2,F3.3),F3.1),F3.3),Comm(Comm(Comm(F3.3,F3.1),F3.2),F3.3),Comm(Comm(Comm(F3.3,F3.2),F3.1),F3.3),];
K3:=F3/B3;
a:=K3.1;
b:=K3.2;
c:=K3.3;
A3:=Subgroup(K3,[a*b*c,Comm(a,b)*Comm(a,c)*Comm(b,c),Comm(Comm(a,b),c),
Comm(Comm(a,c),b)]);

But when I run the command AbelianInvariants(A3), the following error
message appeared:

Error, the coset enumeration has defined more than 4096000 cosets
 called from
TCENUM.CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
CosetTableFromGensAndRels( fgens, grels, fsgens ) called from
TryCosetTableInWholeGroup( H ) called from
CosetTableInWholeGroup( H ) called from
RelatorMatrixAbelianizedSubgroupRrs( G, H ) called from
...  at line 66 of *stdin*
type 'return;' if you want to continue with a new limit of 8192000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit

I thought it was because my groups are too complicated for GAP and thus I
tried a much simpler version of groups:

F2:=FreeGroup("a","b");
B2:=[Comm(Comm(F2.1,F2.2),F2.1),Comm(Comm(F2.1,F2.2),F2.2)];
K2:=F2/B2;
A2:=Subgroup(K2,[K2.1*K2.2,Comm(K2.1,K2.2)])
*
*
When I run the command AbelianInvariants(A2), the same error message
appeared.

As I urgently need to do these calculations, any assistance/advice will be
greatly appreciated. By the way, this is the first time that I write to
this forum; please forgive me if there is anything improper in my question.

Many thanks and best regards,

MH