论文标题
在零的局部紧凑型组上
On locally compact groups with zero
论文作者
论文摘要
我们在G组上研究代数特性，使得离散的G组具有这些特性，那么A相邻零的G上G上的每个局部紧凑型移位连续拓扑是紧凑或离散的。我们介绍了选举灵活的和选举稳定的群体，并建立了它们的特性。特别是，我们证明每个具有无限索引的无限循环亚组和每个不可数的交换群体都是选举灵活的，并表明每个可计数的本地有限群体都是选举稳定的。本文的主要结果是：如果G是一个离散的选举灵活组，则每个Hausdorff局部紧凑的换移 - 连续拓扑在G上具有相邻的零是紧凑的，要么是离散的。同样，我们在任何离散的几乎循环基团（因此在选举稳定的组上）G构建了一个非污染局部紧凑的偏移转移拓扑的局部紧凑型移位拓扑。
We study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible and electorally stable groups and establish their properties. In particular, we prove that every group with an infinite cyclic subgroup of an infinite index and every uncountable commutative group are electorally flexible, and show that every countable locally finite group is electorally stable. The main result of the paper is the following: if G is a discrete electorally flexible group then every Hausdorff locally compact shift-continuous topology on G with adjoined zero is either compact, or discrete. Also, we construct a non-discrete non-compact Hausdorff locally compact shift-continuous topology on any discrete virtually cyclic group (and hence on a electorally stable group) G with adjoined zero.
