Context-Free Groups and Bass–Serre Theory
Context-Free Groups and Bass–Serre Theory
复制标题
上下文无关群和 Bass-Serre 理论
DOI：
10.1007/978-3-319-60940-9_2
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Weiss
中科院分区：
文献类型：
--
作者：
V. Diekert;A. Weiss
一个群生成的词问题是群中等于单位元的生成元上的词的集合。因此，问题一词是一种形式语言。如果这个语言碰巧是上下文无关的，那么这个组就被称为上下文无关的。自动生成的虚拟自由组是上下文无关的。在开创性的论文Muller-Schupp [38]中，证明了匡威的情况：每个上下文自由群都是虚拟自由的。在过去的几十年里，人们发现了上下文无关群的许多其他刻画，这表明上下文无关群在组合群论中起着重要的作用。
The word problem of a finitely generated group is the set of words over the generators that are equal to the identity in the group. The word problem is therefore a formal language. If this language happens to be context-free, then the group is called context-free. Finitely generated virtually free groups are context-free. In the seminal paper Muller–Schupp [38] the converse was shown: every context-free group is virtually free. Over the past decades a wide range of other characterizations of context-free groups have been found. It underlines that context-free groups play a major role in combinatorial group theory.