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Dea Gap-forum, and Chad,

you asked:

> I am interested in working with groups formed by crossing two integer sets.

> For example: Z2 X Z2 = { (0,0), (0,1), (1,0), (1,1)} I am a new user to GAP

> and have looked in the tutorial and the REF files under groups but have

> found nothing. Does anyone know how to do this or can you point me in the

> right direction of where I might look to find out how? Thank you for any

> help you can provide.

If you want to see Z2xZ2 as a group, you can enter:

gap> G:=DirectProduct(CyclicGroup(2),CyclicGroup(2)); <pc group of size 4 with 2 generators> gap> gens:=GeneratorsOfGroup(G); [ f1, f2 ] gap> gens[1]*gens[2]; f1*f2 gap> gens[1]*gens[2]*gens[1]; f2

If you want to see it as an algebra over Z2:

gap> R:=DirectSumOfAlgebras(GF(2),GF(2));

<algebra of dimension 2 over GF(2)>

It should be possible to construct it as a ring (in a way that you can

also treat Z2xZ3 as a ring).

Best wishes,

Jan

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