Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Product of group subsets "ST", then "ST" coincides with the semidirect product of "S" and "T". Finally, if both "S" and "T" are normal in "ST", then "ST" coincides with the direct product of "S" and "T". If "S" and "T" are subgroups whose intersection is the trivial subgroup (identity element) and additionally "ST" = "G", then "S" is called a complement of "T" and vice versa. By a (locally unambiguous) abuse of terminology, two subgroups that intersect only on the (otherwise obligatory) identity are sometimes called disjoint. A question that arises in the case of a non-trivial intersection between a normal subgroup "N"