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
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