  The tensor product of one code endowed with the Hamming metric and one
endowed with the rank metric is analyzed. This gives a code which naturally
inherits the sum-rank metric. Specializing to the product of a cyclic code and
a skew-cyclic code, the resulting code turns out to belong to the recently
introduced family of cyclic-skew-cyclic. A group theoretical description of
these codes is given, after investigating the semilinear isometries in the
sum-rank metric. Finally, a generalization of the Roos and the Hartmann-Tzeng
bounds for the sum rank-metric is established, as well as a new lower bound on
the minimum distance of one of the two codes constituting the product code.
