Show that ijk , ijkl , are tensors under the symmetric group but not under any

Show that δijk

, δijkl

, … are tensors under the symmetric group but not under any larger group.

[The symmetric group, which is most conveniently represented by the set of permutation matrices, arises naturally in the study of sample moments based on simple random samples, where the order in which the observations are recorded is assumed to be irrelevant. See Chapter 4.]