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.
DFG Programme
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