Wagner was born in
Saratov and studied at
Moscow State University, where
Veniamin Kagan was his advisor. He became the first geometry chair at
Saratov State University. He received the
Lobachevsky Medal in 1937. Wagner was also awarded "the
Order of Lenin, the
Order of the Red Banner, and the title of Honoured Scientist RSFSR. Moreover, he was also accorded that rarest of privileges in the USSR: permission to travel abroad." Wagner is credited with noting that the collection of
partial transformations on a set
X forms a semigroup \mathcal{PT}_X which is a subsemigroup of the semigroup \mathcal{B}_X of
binary relations on the same set
X, where the semigroup operation is
composition of relations. "This simple unifying observation, which is nevertheless an important psychological hurdle, is attributed by Schein (1986) to V.V. Wagner." ==See also==