[GAP Forum] How can I get the elements of a free product?

[Nikos Apostolakis]

Dear Forum,

I want to construct the free product of n copies of ZZ/2 and work with its
elements.  I get some strange behavior that I can't quite understand:

F := n -> FreeProduct(List([1..n], i -> CyclicGroup(2))); #==> function( n
) ... end
G := n -> GeneratorsOfGroup(F(n)); #==> function( n ) ... end
G(3)[2] in G(3); #==> false
G(3)[2] in F(3); #==> false

However:

GeneratorsOfGroup(F(3)); #==> [ f1, f2, f3 ]
last[1]^2*last[2] = last[2]; #==> true

which is what I would expect if GeneratorsOfGroup(F(3)) gives elements of
the free product.

I wonder if somebody could explain this behavior? Also how can I actually
get what I want?

Thanks a lot for any help,
Nikos