Symmetries and structure in the fp shell and g_9/2 shell

First in a single-j-shell calculation (j = f_7/2) we discuss various symmetries, e.g., two to one in ⁴⁴Ti vs ⁴³Ti. We note that the wave function amplitudes for T(higher) states are coefficients of fractional parentage, and that orthogonality of T(higher) and T(lower) states leads to useful results. Then we consider what happens if T = 0 two-body matrix elements are set equal to zero. We find a partial dynamical symmetry with several interesting degeneracies. It is noted that some formulae developed for identical particles also apply to different (companion) problems involving mixed systems of protons and neutrons. In the g_9/2 shell, where one can have for the first time seniority violation for identical particles, we find some interesting yet unproven results.