In the question i forgot to mention that G is transitive on A(sorry for that).
with this in mind there exists a
for such a g there exists a bijection:
Uuh?? You define a function between two sets naming it the same as an element in G? And besides this,
how is the function defined? Because we know that , but what happens with some
How's defined the map you're talking about on x? Can you be sure that
to begin with at all? So, how do you define the map ?
to prove this consider
now
from my first post
to show that the mapping is injective i must show that
i will use contradiction to do so. Assume
which is a contradiction. so the map is injective.
has the injection been shown correctly? If this is correct then i can attempt to show the surjection too. Please comment.