relative infinite general linear group and projection
Proposition
Let 
be a ring, 
an ideal and 
the relative infinite general linear group.
Then
is a group-isomorphism
see:
Proof
a)
Let
be an element of 
.
Then by definition of 
we have
and by definition of 
we know that 
(cf. explicite description of a pullback of a ring and ideal)
This shows that
Thus the map is welldefined.
It follows that this map is a bijection
