群的对称生成的新进展
Recent Progress in the Symmetric Generation of Groups
摘要：
许多群具有高度对称的生成集，这些生成集自然地被赋予了潜在的组合结构。这样的生成集可以证明是非常有用的，无论是在理论上提供新的存在性证明的群体和实际上提供简洁的手段表示群元素。我们给出了一个调查的结果，在这些对称生成集的研究。为了与早先关于这个问题的调查保持一致，我们强调零星的单群。附录：这是一个最新版本的调查文章最初接受列入2009年“集团圣安德鲁斯”会议的议事录。自从这篇文章被接受后，作者已经意识到这个主题的其他最近的工作，我们在这里提供了一个更新的版本（最值得注意的是第3.4节的内容）。
英文摘要：
Many groups possess highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for groups and practically by providing succinct means of representing group elements. We give a survey of results obtained in the study of these symmetric generating sets. In keeping with earlier surveys on this matter, we emphasize the sporadic simple groups. ADDENDUM: This is an updated version of a survey article originally accepted for inclusion in the proceedings of the 2009 `Groups St Andrews' conference. Since the article was accepted the author has become aware of other recent work in the subject that we incorporate to provide an updated version here (the most notable addition being the contents of Section 3.4.)
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