[GAP Forum] Presentation of a group

[William Giuliano]

Dear Forum,
                    I have written the presentation of two groups, which I
am quite sure are the Mathieu group M_24 and the Held group. The problem I
have is the message I get when I try to find their orders:

#I  Coset table calculation failed -- trying with bigger table limit

#I  Coset table calculation failed -- trying with bigger table limit

Error, reached the pre-set memory limit

(change it with the -o command line option) in

  g[2 * limit] := 0;


I don't know if this is an indication of an actual error in my presentation
or something which has to do with GAP. Here is one of the presentations

gap>
f:=FreeGroup("a_1","a_2","a_3","a_4","a_5","a_6","a_7","a_8","a_9","a_10","a_11","a_12","a_13");

<free group on the generators [ a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8,
a_9, a_10, a_11, a_12, a_13 ]>

gap>
r:=[f.1^2,Comm(f.1,f.3)*f.2^(-1),Comm(f.1,f.5)*f.4^(-1),Comm(f.1,f.8)*f.7^(-1),Comm(f.1,f.9),Comm(f.1,f.10),Comm(f.1,f.12),Comm(f.1,f.13)*f.6^(-1),

>
f.2^2,Comm(f.2,f.6)*f.4^(-1),Comm(f.2,f.8),Comm(f.2,f.9)*f.7^(-1),Comm(f.2,f.10),Comm(f.2,f.11)*f.1^(-1),Comm(f.2,f.13)*(f.4*f.5)^(-1),

>
f.3^2,Comm(f.3,f.6)*f.5^(-1),Comm(f.3,f.7),Comm(f.3,f.9)*f.8^(-1),Comm(f.3,f.10),(f.3*f.11)^3,Comm(f.3,f.13)*f.4^(-1),

>
f.4^2,Comm(f.4,f.8),Comm(f.4,f.9),Comm(f.4,f.10)*f.7^(-1),Comm(f.4,f.12)*f.2^(-1),

>
f.5^2,Comm(f.5,f.7),Comm(f.5,f.9),Comm(f.5,f.10)*f.8^(-1),Comm(f.5,f.11)*f.6^(-1),Comm(f.5,f.12)*f.3^(-1),

> f.6^2,Comm(f.6,f.7),Comm(f.6,f.8),Comm(f.6,f.10)*f.9^(-1),(f.6*f.12)^3,

> f.7^2,Comm(f.7,f.11),Comm(f.7,f.12),Comm(f.7,f.13)*f.4^(-1),

> f.8^2,Comm(f.8,f.11)*f.9^(-1),Comm(f.8,f.12),Comm(f.8,f.13)*f.5^(-1),

> f.9^2,Comm(f.9,f.12)*f.10^(-1),Comm(f.9,f.13)*f.6^(-1),

> f.10^2,Comm(f.10,f.11),(f.10*f.13)^3,

> f.11^2,(f.11*f.12)^4,Comm(f.11,f.13)*(f.6*f.4)^(-1),

> f.12^2,(f.12*f.13)^5,

> f.13^2,(f.6*f.12*f.13)^5,(f.10*f.13*f.12)^5];;

gap> g:=f / r;

<fp group on the generators [ a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9,
a_10, a_11, a_12, a_13 ]>


Thanks
Best regards,
William