论文标题
有限阿贝尔小组的完整分裂
The complete splittings of finite abelian groups
论文作者
论文摘要
令$ g $为有限的组。我们会说，如果每个元素（非零元素）$ g $的$ g $ of $ g $ of $ g $ g $ g = ms $ g = ms $，则$ g = ms $ in m $ in m $ in m $和$ 0 $ 0 $ 0 $ 0，在本文中，我们确定有限阿贝尔群体的完整分裂的结构。特别是，对于循环组的完整分裂，我们的描述更具体。此外，我们为循环基团的完整分裂的存在和不存在结果显示了一些结果，并找到了有限组的完整分裂和分裂之间的关系。
Let $G$ be a finite group. We will say that $M$ and $S$ form a \textsl{complete splitting} (\textsl{splitting}) of $G$ if every element (nonzero element) $g$ of $G$ has a unique representation of the form $g=ms$ with $m\in M$ and $s\in S$, and $0$ has a such representation (while $0$ has no such representation). In this paper, we determine the structures of complete splittings of finite abelian groups. In particular, for complete splittings of cyclic groups our description is more specific. Furthermore, we show some results for existence and nonexistence of complete splittings of cyclic groups and find a relationship between complete splittings and splittings for finite groups.
