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Based on evolutionary computations of 90 stellar models, we have analysed the impact of initial composition and core overshooting on the post-He-burning evolution and the associated nucleosynthesis of Super-AGB stars, pointing particular attention on the C-burning phase. Moreover the possible link between the transition masses , and (defined as the critical initial mass above which C-burning ignites, the minimum initial mass for an electron-capture supernova and the minimum initial mass for the completion of all the nuclear burning phases respectively) and the properties of the core during the core He-burning phase is also briefly discussed.

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