  We discuss the Kummer subspaces of tensor products of cyclic algebras,
focusing mainly on the case of cyclic algebras of degree 3. We present a family
of maximal spaces in the general case, classify all the monomial spaces in the
case of tensor products of cyclic algebras of degree 3 using graph theory, and
provide an upper bound for the dimension in the generic tensor product of
cyclic algebras of degree 3.
