  We analyze the divisibility properties of generalized Pauli dynamical maps.
Using the results for image non-increasing dynamical maps, we formulate the
conditions for the underlying evolution to satisfy specific non-Markovianity
criteria. For the qubit evolution, we find the necessary and sufficient
conditions for P and CP-divisibility of the associated, in general
noninvertible, Pauli dynamical maps. Finally, we analyze the divisibility
degree for mixtures of noninvertible phase-damping channels. For P-divisible
maps, we propose a legitimate time-local generator with all temporarily
infinite decoherence rates.
