Probabilistic Generation of Wreath Products of Non-abelian Finite Simple Groups
Probabilistic Generation of Wreath Products of Non-abelian Finite Simple Groups
复制标题
非阿贝尔有限单群花环乘积的概率生成
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
M. Quick
中科院分区：
文献类型：
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作者：
M. Quick
摘要 我们证明，当第一个单群的阶数趋于无穷时，生成非交换有限单群的迭代标准花环积的概率为正且趋于 1。其结果是，作为这些迭代花环乘积的逆极限的有限群是正有限生成的。整个过程中使用的信息取决于有限简单群的分类。
Abstract We show that the probability of generating an iterated standard wreath product of non-abelian finite simple groups is positive and tends to 1 as the order of the first simple group tends to infinity. This has the consequence that the profinite group which is the inverse limit of these iterated wreath products is positively finitely generated. Information depending on the Classification of Finite Simple Groups is used throughout.