Abstract There are only 10 Euclidean forms, that is flat closed three-dimensional manifolds: six are orientable and four are non-orientable. The aim of this paper is to describe all types of n-fold coverings over orientable Euclidean manifolds and and calculate the numbers of nonequivalent coverings of each type. We classify subgroups in the fundamental groups and up to isomorphism and calculate the numbers of conjugated classes of each type of subgroups for index n. The manifolds and are uniquely determined among the others orientable forms by their homology groups and

中文翻译：

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关于封闭可定向欧几里得流形 G2 和 G4 的覆盖

摘要 欧几里得形式只有10种，即平面封闭的三维流形：6种可定向，4种不可定向。本文的目的是描述可定向欧几里得流形上所有类型的 n 重覆盖，并计算每种类型的非等价覆盖的数量。我们将子群分类为基本群和同构，并计算索引 n 的每种类型子群的共轭类数。流形 和 由它们的同源群和其他可定向形式唯一确定