Abstract We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective space. Natural examples of such groups of germ maps are given by holonomy groups and monodromy groups of integrable systems (foliations) under certain conditions. We prove some finiteness results for these groups extending previous results in [D. Cerveau and F. Loray, Un théorème de Frobenius singulier via l’arithmétique élémentaire, J. Number Theory 68 1998, 2, 217–228]. Applications are given to the framework of germs of holomorphic foliations. We prove the existence of first integrals under certain irreducibility or more general conditions on the tangent cone of the foliation after a punctual blow-up.

中文翻译：

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全纯叶理的不可约完整群和第一积分

摘要 我们研究具有称为不可约性的特性的复杂微分同胚的细菌群。这个概念是由复杂射影空间中不可约超曲面的补集的基本群的相似性质所激发的。这种细菌图谱组的自然例子是在某些条件下由可积系统（叶）的完整组和单向组给出的。我们证明了这些组的一些有限性结果扩展了 [D. Cerveau 和 F. Loray, Un théorème de Frobenius singulier via l'arithmétique élémentaire, J. Number Theory 68 1998, 2, 217–228]。对全纯叶面的胚芽框架进行了应用。