  We study the measurement-induced geometric discord based on the trace norm
and generalize some properties known for qutrits to qudits. Previous
preliminary results for bipartite qutrit systems (i.e. d=3 systems) are here
strictly proved for arbitrary d. Present study supports observations, coming
also from other approaches, that systems with $d \geq 3$ show similar behaviour
when quantum correlations are concerned, but there is pronounced difference
between d=2 and d=3. Qubit systems are exceptionally simple. Underlying
geometry of state spaces and related Lie groups are responsible for that.
