Here is an excerpt.
Now consider [the multiplication table of] the group with three distinct elements:
. The only products which we must determine explicitly are
,
,
, and
since all other products involve the unit
. The product
cannot equal
or
, since that would imply that either
or
, respectively. Thus,
. The Cancellation Theorem then
requires that
[The book misprints this equation.],
, and
.
My problem is that I can't justify to myself the last sentence. Please help explain.
P.S.
Emmy Noether is German.
