# How to get a tuple representation of a DirectProduct in GAP? [closed]

Question.
Is there any way to get and use a tuple representation of a DirectProduct?

Explaination.
Let's assume we have groups $$G, H$$ which are cyclic group and symmetric group respectively. Let's take $$L$$ as a direct product of $$G$$ and $$H$$. I am aware of Projection and Embedding functions as the example below presents.

gap> G := CyclicGroup(6);
<pc group of size 6 with 2 generators>
gap> H := SymmetricGroup(6);
Sym( [ 1 .. 6 ] )
gap> L := DirectProduct(G,H);
<group of size 4320 with 4 generators>
gap> Embedding(L,1);
MappingByFunction( <pc group of size 6 with
2 generators>, <group of size 4320 with 4 generators>, function( elm ) ... end )
gap> Image(Embedding(L,1));
<group of size 6 with 2 generators>
gap> Image(Embedding(L,2));
<group of size 720 with 2 generators>
gap>


My goal is to take an exact element of $$g \in G$$ and $$h \in H$$ and get an element $$(g,h) \in L$$. I have noticed there is an object called DirectProductElement, but there is no documentation about it.

• @DerekHolt, Don't you mean? Image(Embedding(L, 1), GeneratorsOfGroup(G)[1]);? May 19 at 14:12
• So, either I do not understand or your code does not compile. May 19 at 14:51
• OK, I'll write it as an answer, using your example. May 19 at 14:57

gap> G := CyclicGroup(6);;

• This is the answer that works and it gives what I wanted. Actually, getting back to your comment. In your comment m1 was not Embedding, but an Image. That's the reason, I doubt your code in your comment will work. Thank you Derek! May 19 at 15:01