Strongly dense free subgroups of semisimple algebraic groups
Strongly dense free subgroups of semisimple algebraic groups
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半简单代数群的强稠自由子群
作者：
E. Breuillard;B. Green;R. Guralnick;T. Tao
我们证明了（除了一个可能的例外）在一个足够大的域上的任何半单代数群中存在强稠密自由子群。这些都是非交换自由子群，所有的子群要么是循环的，要么是Zubalki稠密的。作为结果，我们得到了李型有限单群的新的生成结果，并加强了与Hausdorff-Banach-Tarski悖论有关的Borel定理。在本文的续篇中，我们利用这个结果建立了有限个李型单群上的随机Cayley图的一致展开性质
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type
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作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal
通讯作者：
Nina E. Menezes;M. Quick;C. Roney-Dougal