  We study the representations of the infinite symmetric group induced from the
identity representations of Young subgroups. It turns out that such induced
representations can be either of type~I or of type~II. Each Young subgroup
corresponds to a partition of the set of positive integers; depending on the
sizes of blocks of this partition, we divide Young subgroups into two classes:
large and small subgroups. The first class gives representations of type I, in
particular, irreducible representations. The most part of Young subgroups of
the second class give representations of type~II and, in particular, von
Neumann factors of type II. We present a number of various examples. The main
problem is to find the so-called {it spectral measure of the induced
representation.} The complete solution of this problem is given for two-block
Young subgroups and subgroups with infinitely many singletons and finitely many
finite blocks of length greater than one.
