A note on Moufang sets

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.