  The paper deals with recursive constructions for simple 3-designs based on
other 3-designs having $(1, \sigma)$-resolution. The concept of $(1,
\sigma)$-resolution may be viewed as a generalization of the parallelism for
designs. We show the constructions and their applications to produce many
previously unknown infinite families of simple 3-designs.
  We also include a discussion of $(1,\sigma)$-resolvability of the constructed
designs.
