  We study the induced measure obtained from a 1-step Markov measure, supported
by a topological Markov chain, after the mapping of the original alphabet onto
another one. We give sufficient conditions for the induced measure to be a
Gibbs measure (in the sense of Bowen) when the factor system is again a
topological Markov chain. This amounts to constructing, when it does exist, the
induced potential and proving its Holder continuity. This is achieved through a
matrix method. We provide examples and counterexamples to illustrate our
results.
