论文标题
随机生成汤普森的团体$ f $
Random Generation of Thompson's group $F$
论文作者
论文摘要
我们证明，在两个天然概率模型（由Cleary，Elder，Rechnitzer和Taback研究）下，汤普森组$ f $的随机元素产生整个组的可能性为正。我们还证明，对于任何包含$ f $的“天然”副本的任何$ k $生成的子组$ h $ of $ f $，随机$（k+2）$的概率（k+2）$ - 生成的子组与$ f $ comcinted a $ h $ comcinting agy agent。
We prove that under two natural probabilistic models (studied by Cleary, Elder, Rechnitzer and Taback), the probability that a random pair of elements of Thompson's group $F$ generate the entire group is positive. We also prove that for any $k$-generated subgroup $H$ of $F$ which contains a "natural" copy of $F$, the probability of a random $(k+2)$-generated subgroup of $F$ coinciding with $H$ is positive.
