Direct products

To compute the direct product of two or more groups, Magma provides the function DirectProduct. This function returns a group that is isomorphic to the direct product of the given groups, along with two lists of homomorphisms. The first list contains the embeddings of the original groups into the direct product, and the second list contains the projections from the direct product onto the original groups.

C2 := CyclicGroup(2);;
C4 := CyclicGroup(4);;
G, a, b := DirectProduct(C2,C4);

The group G is C2*C4, and the variable a is the following list:

[
    Mapping from: GrpPerm: C2 to GrpPerm: G,
    Mapping from: GrpPerm: C4 to GrpPerm: G
]
> b;
[
    Mapping from: GrpPerm: G to GrpPerm: C2,
    Mapping from: GrpPerm: G to GrpPerm: C4
]

We can also send a list of groups to the function DirectProduct. Here is an example:

G := DirectProduct([C2,C4,C2,C2]);