Hi David,
On Jul 31, 4:47 pm, David Joyner <wdjoy...@gmail.com> wrote:
> Maybe I don't understand your question. It seems you are claiming that
> if G is a permutation group and H is a normal subgroup then
> the quotient G/H embeds into G. Are you sure that is true?
> ...
> > Where do the 5 and 6 suddenly come from? In my understanding the
> > elements of the quotient group G/H are classes of elements of G, which
> > operates on {1, 2, 3, 4}.
I understand the question like this: The elements of G/H are *sets* of
elements of G (namely cosets). One obvious way to represent a coset is
by picking one of its elements -- hence, an element of G. Then, it is
indeed surprising that higher numbers occur.
Aparently G.quotient_group(H) returns a permutation group that is
isomorphic to G/H. And then, it is of course not surprising that it
does not simply act on {1,2,3,4}.
But the following question arises:
Start with
sage: G = SymmetricGroup(4)
sage: H = G.normal_subgroups()[1]
sage: H
Permutation Group with generators [(1,3)(2,4), (1,4)(2,3)]
sage: X= G.quotient_group(H)
Given an element g of G, how can one find the element of X that
corresponds to the coset of g wrt. H ?
sage: X(g)
would in general not work!
How can one construct the map from G to X that corresponds to taking
the quotient by H ?
Cheers,
Simon
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