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The Z(N) dependence of the pure Yang-Mills gluon propagator, in the Landaugauge, is investigated at finite temperature for N=3. Special attention will begiven to the behaviour near the critical temperature $T_c$. Our simulationsshow a complex pattern as expected in a first order phase transition.Furthermore, we identify an order parameter directly associated with thebreaking of the SU(3) center symmetry.

Z(N) dependence of the pure Yang-Mills gluon propagator in the Landau gauge near Tc