论文标题
共养和有限的恩托 - 刚分离混合阿贝尔群
Co-Hopfian and boundedly endo-rigid mixed abelian groups
论文作者
论文摘要
对于给定的红衣主教$λ$和扭转的Abelian Group $ K $的基数小于$λ$，我们在某些温和条件下（例如$λ=λ=λ^{\ aleph_0} $），有必要的endo-rigid abelian abelian $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ g $ cascinality $λ$（g tor $ tor（g）= k $。本质上，我们给出了此类对$（k，λ）$的完整表征。除其他外，我们使用了两个版本的黑匣子。我们介绍了构造有限的内岩艾比亚利亚群体的应用。也就是说，我们转向给定规模的共依恋阿贝尔群体的现有问题，并提出了一些新的类别，主要是在混合的阿贝尔群体中。特别是，我们提供了有用的标准，以检测何时有限的内核Abelian群体是共同的，并完全确定红衣主教$λ> 2^{\ aleph_ {0}} $，其中有一个共同求助于$λ$的共同养蜂ABELIAN集团。
For a given cardinal $λ$ and a torsion abelian group $K$ of cardinality less than $λ$, we present, under some mild conditions (for example $λ=λ^{\aleph_0}$), boundedly endo-rigid abelian group $G$ of cardinality $λ$ with $Tor(G)=K$. Essentially, we give a complete characterization of such pairs $(K, λ)$. Among other things, we use a twofold version of the black box. We present an application of the construction of boundedly endo-rigid abelian groups. Namely, we turn to the existing problem of co-Hopfian abelian groups of a given size, and present some new classes of them, mainly in the case of mixed abelian groups. In particular, we give useful criteria to detect when a boundedly endo-rigid abelian group is co-Hopfian and completely determine cardinals $λ> 2^{\aleph_{0}}$ for which there is a co-Hopfian abelian group of size $λ$.
