Lumpability and Absorbing Markov Chains By

We consider an absorbing Markov Chain that a result of an aggregation finite Markov Chain of higher dimension with respect to the partition)(tY)(tX A and unknown transition probability matrix (t.p.m) P, the question of whether is(not) also absorbing will be study for the lumped and the weakly lumped absorbing Markov Chain for all (certain) partitions within isomorphic with respect to the cases (k, k+1) and (2, k). Special cases will be introduced for each case, for each partition.)(t