论文标题
C最佳拓扑组
C-Minimal topological groups
论文作者
论文摘要
我们研究所有封闭亚组（完全）最小的拓扑组，我们称之为C-（完全）最小的组。我们表明，局部紧凑的C微连接组是紧凑的。使用霍尔和库拉蒂拉卡的著名定理，以及由于粗暴和赫尔福特的特征，我们证明了C最低限度的本地可解决的谎言组是紧凑的。结果表明，如果一个拓扑组$ g $包含紧凑的开放式亚组$ n $，则$ g $在且仅当$ g/n $ h $ heradity上是不可遗传的，而$ g $是最小的。此外，必须紧凑的一个完全可溶解或强覆盖的C-量最小的组。反对Dikranjan和Megrelishvili的一个问题，我们发现一个完全不紧凑的谎言群体完全可解决（甚至是Metabelian）的谎言群体。我们还证明，$ a \ times f $是c-（完全）最小的（分别）最小的Abelian Group $ a $ a $和每个有限的集团$F。$。
We study topological groups having all closed subgroups (totally) minimal and we call such groups c-(totally) minimal. We show that a locally compact c-minimal connected group is compact. Using a well-known theorem of Hall and Kulatilaka and a characterization of a certain class of Lie groups, due to Grosser and Herfort, we prove that a c-minimal locally solvable Lie group is compact. It is shown that if a topological group $G$ contains a compact open normal subgroup $N$, then $G$ is c-totally minimal if and only if $G/N$ is hereditarily non-topologizable. Moreover, a c-totally minimal group that is either complete solvable or strongly compactly covered must be compact. Negatively answering a question by Dikranjan and Megrelishvili we find, in contrast, a totally minimal solvable (even metabelian) Lie group that is not compact. We also prove that the group $A\times F$ is c-(totally) minimal for every (respectively, totally) minimal abelian group $A$ and every finite group $F.$
