There are different notions of homology and cohomology that can be defined for a group with an action of another group by group automorphisms. In this paper we address three natural questions that arise in this context. Namely, the relation of these notions with the usual (co)homology of a semidirect product, the interpretation of the first homology group as some kind of abelianization and the classification of (invariant) group extensions.

中文翻译：

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关于群的不变（共）同源性

可以通过群自同构为具有另一个群的动作的群定义不同的同源性和上同调概念。在本文中，我们解决了在这种情况下出现的三个自然问题。即，这些概念与半直积的通常（共）同调的关系，将第一个同调群解释为某种阿贝尔化和（不变）群扩展的分类。