twinic群的超扩张代数
Algebra in superextensions of twinic groups
摘要：
给定一个群$X$，研究了由$X$上的极大链系构成的紧右拓扑半群$λ(X)$的代数结构.这个半群包含超滤子半群$β(X)$作为闭子半群。我们构造了半群$λ(X)$在$X$幂集的所有自映射半群中的一个忠实表示，并利用这个表示刻画了$X$的每一个孪生群的$λ(X)$的极小理想和极小左理想的结构.孪生群类包括所有顺从群和所有具有周期生成元的群，但不包括具有两个生成元的自由群。
英文摘要：
Given a group $X$ we study the algebraic structure of the compact right-topological semigroup $λ(X)$ consisting of maximal linked systems on $X$. This semigroup contains the semigroup $β(X)$ of ultrafilters as a closed subsemigroup. We construct a faithful representation of the semigroup $λ(X)$ in the semigroup of all self-maps of the power-set of $X$ and using this representation describe the structure of minimal ideal and minimal left ideals of $λ(X)$ for each twinic group $X$. The class of twinic groups includes all amenable groups and all groups with periodic commutators but does not include the free group with two generators.
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