  We show that the transition function of the cascaded connection of two FSRs
can be viewed as a wreath product element. This allows us to study periods of
cascaded connections with algebraic methods, obtaining both a general,
nontrivial upper bound on the maximum period of a cascaded connection and a
complete, explicit understanding of the periods in the important case of the
cascaded connection of an $n$-dimensional De Bruijn sequence into an
$m$-dimensional linear FSR.
