  The notion of Moufang set was introduced by Jacques Tits in \cite{Tits92}. We
recall briefly the well-established definition and a construction which, under
certain conditions, yields a Moufang set. We show that these conditions can be
considerably relaxed, leading to a set of conditions which is easier to verify.
In the second part, we consider isomorphisms of Moufang sets and prove that
Moufang sets constructed from isomorphic groups are indeed isomorphic as
Moufang sets.
