Hello! I want to compute the abelianization of the kernel of the map F->G, where F is finitely presented group with generators a_1, ..., a_10 and relations a_1^2=...=a_10^2=e, a_1*a_2*a_3*a_4*a_5=a_6*a_7*a_8*a_9*a_10=e, G is abelian group (Z/2)^4 with basis e_1,...,e_4. The map is given by images a_1->e_1, a_2->e_2, a_3->e_3, a_4->e_4, a_5->e_1*e_2*e*3*e_4, a_6->e_2*e_3*e_4, a_7->e_1*e_3*e_4, a_8->e_1*e_3, a_9->e_2*e_4, a_10->e_3*e_4.
I realize it by the following code: f:=FreeGroup(10); F:=f/[f.1^2,f.2^2,f.3^2,f.4^2,f.5^2,f.6^2,f.7^2,f.8^2,f.9^f,f.10^2,f.1*f.2*f.3*f.4*f.5,f.6*f.8*f.8*f.9*f.10]; G:=Group((1,2),(3,4),(5,6),(7,8)); hom:=GroupHomomorphismByImages(F,G,[F.1,F.2,F.3,F.4,F.5,F.6,F.7,F.8,F.9,F.10],[(1,2),(3,4),(5,6),(7,8),(1,2)(3,4)(5,6)(7,8),(3,4)(5,6)(7,8),(1,2)(5,6)(7,8),(1,2)(5,6),(3,4)(7,8),(5,6)(7,8)]); iso:=IsomorphismFpGroup(Kernel(hom)); h:=Range(iso); comm:=CommutatorFactorGroup(h); Order(comm); But it says, that the order is infinity, but it is obviously impossible, because it is finitely generated subgroup by elements of order 2. Thank you, Yakov Kononov. _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
