[GAP Forum] Question

[Alexander Hulpke]

Dear Forum,

> Dear members,   I would like to know how we can build the group G=<a,b,c | a^2=b^2=c^2=1, abc=bca=cab> in gap.

`ParseRelators' is probably the most convenient way to enter such relations:

gap> f:=FreeGroup("a","b","c");
<free group on the generators [ a, b, c ]>
gap> rels:=ParseRelators(f,"a2=b2=c2,abc=bca=cab");
[ b^2*a^-2, c^2*a^-2, b*c*a*c^-1*b^-1*a^-1, c*a*b*c^-1*b^-1*a^-1 ]
gap> g:=f/rels;
<fp group on the generators [ a, b, c ]>

Now g is the desired group.

Best,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke