| 摘 要： | In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in 7] and a weak Hopf algebra introduced in 2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak(H, A)Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.
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