[GAP Forum] quotient group homomorphisms

[Walter Becker]

The question here is how to display the mapping (homomorphism)

h:G---->G/N[i] 

on the generators of the group G. For a specific case try this:

 

G is Ho,(C_4 X C_2)  this is group number 259  in the Hall-Senior

Tables and group number 138 in the Small group Library.

 

A specific presentation here is 

 

f:=FreeGroup("a", "b", "c"  );
g:=f/[f.1^2,
      f.2^2,
      f.3^2,
      (f.1^-1*f.2^-1*f.1*f.2)^2,
      (f.1^-1*f.3^-1*f.1*f.3)^2,
       (f.2^-1*f.3^-1*f.2*f.3),
(f.1^-1*f.2^-1*f.1*f.2)^-1*f.3^-1*(f.1^-1*f.2^-1*f.1*f.2)*f.3*
((f.1^-1*f.3^-1*f.1*f.3)^-1*f.2^-1*(f.1^-1*f.3^-1*f.1*f.3)*f.2)^-1   
];

 

The subgroups of most interest here are (C_2 X C_2)wr C_2

of order 32 of which there are 3 cases.

 

Most specivically what are the images 

h(f.1), h(f.2)  and h(f.3).

 

Thanks  

 

Walter Becker