Algorithmic aspects of branch groups

分支群构成了无限群的一个基本类，并包括一些重要的例子，如中间词增长的“Grigorchuk群”和“Gupta-Sidki群”--这些都是无限扭群的例子。虽然大多数算法问题在一般类别的群中是不可解的，例如通过有限表示(例如识别平凡的、有限的或同构的子群)给出的那些问题，但是已经开发了许多有用的工具来处理特定类别的组，并且它们在实践中表现良好。特别是，在双曲群和矩阵群上都有令人满意的算法。该提议将算法群论的领域扩展到自相似群的方向：特别是将解决字问题、共轭问题、同构问题和递归表示的构造(“L表示”)的这些群的解，并考虑到效率和实际实现。

Branch groups form a basic class of infinite groups, and include such important examples as the “Grigorchuk group”' of intermediate word-growth and the “Gupta-Sidki groups'' — all examples of infinite torsion groups. Although most algorithmic problems are unsolvable in the general class of groups, e.g. those given by a finite presentation (recognizing trivial, finite, or isomorphic subgroups, e.g.), many useful tools have been developed to deal with specific classes groups, and they perform well in practice. In particular, there are satisfactory algorithms that operate on hyperbolic groups and on matrix groups. The proposal will extend the realm of algorithmic group theory in the direction of self-similar groups: in particular, solutions for these groups of the word problem, the conjugacy problem, the isomorphism problem, and the construction of recursive presentations (“L-presentations”) will be addressed, with efficiency and actual implementation in mind.