  We establish relations between representation dimensions of two algebras
connected by a Frobenius bimodule or extension. Consequently, upper bounds and
equality formulas for representation dimensions of group algebras, symmetric
separably equivalent algebras and crossed products are obtained. Particularly,
for any subgroup H of a finite group G, if [G:H] is invertible in a field, then
the representation dimensions of the group algebras of G and H over the field
are the same.
