  The aim of the present study is to show that: the redefinition of the
factorization scale $Q_i\to z_i Q_i$ in the ladder can be traded exactly for
the NLO correction to the LO evolution kernel, $P(z)\to P(z)+(2C_F
\alpha_S/\pi)\Delta(z)$ The above observation was done/exploited in the
literature, but the present study demonstrates how this phenomenon is realized
within the Markovian Monte Carlo parton shower - hence it might be relevant in
MC practice.
