...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Journal of algebraic combinatorics >On some universal construction of minimal topological generating sets for inverse limits of iterated wreath products of non-Abelian finite simple groups
【24h】

On some universal construction of minimal topological generating sets for inverse limits of iterated wreath products of non-Abelian finite simple groups

机译：关于非阿贝尔有限简单群迭代花圈乘积的逆极限的最小拓扑生成集的一些通用构造

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Let be an arbitrary sequence of non-Abelian finite simple transitive permutation groups. By using the combinatorial language of time-varying automata, we provide an explicit and naturally defined construction of a two-element set which generates a dense subgroup in the inverse limit of iterated permutational wreath products of the groups . The corresponding automaton is equipped with three states, one of which is neutral and the semigroup generated by the other two states is free. We derive other algebraic and geometric properties of the group generated by this automaton. By using the notion of a Mealy automaton, we obtain the analogous construction for the infinite permutational wreath power of an arbitrary non-Abelian finite simple transitive permutation group on a set . We show that the wreath power contains a dense 2-generated not finitely presented amenable subgroup of exponential growth, which is generated by a 3-state Mealy automaton over the alphabet . The self-similar group generated by this automaton is self-replicating, contracting and regular weakly branch over the commutator subgroup.
机译：设为非阿贝尔有限简单传递性置换群的任意序列。通过使用时变自动机的组合语言，我们提供了一个由两个元素组成的显式且自然定义的构造，该集合在组的迭代置换花圈乘积的逆极限中生成一个密集的子组。相应的自动机配备了三个状态，其中一个是中性的，而由其他两个状态生成的半群是自由的。我们导出由该自动机生成的组的其他代数和几何性质。通过使用Mealy自动机的概念，我们获得了集合上任意非阿贝尔有限简单传递性置换群的无限置换花圈能力的类似构造。我们证明了花环幂包含一个密集的2生成的不成比例地呈现的宜人的指数增长子组，该子组是由字母表上的3状态Mealy自动机生成的。该自动机产生的自相似基团是自我复制，收缩并且在换向器子组上有规律地弱分支。

著录项

相似文献

  • 外文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号