[GAP Forum] Question regarding quotient group functions

[Alexander Hulpke]

Dear Daniel Grayham,

> Subgroup(G, [a^2]); 
> where a is one of the generators of the group and say, a^2 has order 2 for example (generates subgroup isomorphic to C2) 
> I get the error:
> Error, families of <gens> and <M> are different

This looks as if a is an element of the free group F, and G a finitely presented group which was a quotient of F. These are incompatible objects. You should use
gens:=GeneratorsOfGroup(G);
a:=gens[1]; # or appropriate

or

AssignGeneratorVariables(G);

to use the correct elements. See the manual section on finitely presented groups
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP045.htm
for more information.

> 
> RightCosets(G, [a^2]); gives an error however:

Wrong syntax. The second argument must be a subgroup, not an element list.

Best wishes,

  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