  We explore new IR phenomena and dualities, arising for product groups, in the
context of N=1 supersymmetric gauge theories. The RG running of the multiple
couplings can radically affect each other. For example, an otherwise IR
interacting coupling can be driven to be instead IR free by an arbitrarily
small, but non-zero, initial value of another coupling. Or an otherwise IR free
coupling can be driven to be instead IR interacting by an arbitrarily small
non-zero initial value of another coupling. We explore these and other
phenomena in N=1 examples, where exact results can be obtained using
a-maximization. We also explore the various possible dual gauge theories, e.g.
by dualizing one gauge group with the other treated as a weakly gauged flavor
symmetry, along with previously proposed duals for the theories deformed by
A_k-type Landau-Ginzburg superpotentials. We note that this latter duality, and
all similar duality examples, always have non-empty superconformal windows,
within which both the electric and dual A_k superpotentials are relevant.
