Algorithmic problems in groups with quadratic Dehn function

[摘要] We construct and study finitely presented groups with quadratic Dehn function (QD-groups) and present the following applications of the method developed in our recent papers. (1) The isomorphism problem is undecidable in the class of QD-groups. (2) For every recursive function fff, there is a QD-group GGG containing a finitely presented subgroup HHH whose Dehn function grows faster than fff. (3) There exists a group with undecidable conjugacy problem but decidable power conjugacy problem; this group is QD.

[学科分类] 神经科学

[关键词] Generators and relations in groups;finitely presented groups;the Dehn function of a group;algorithm;S-machine;van Kampen diagram