Geodesic
Algorithmic problems in groups with quadratic Dehn function
Alexander Yu. Olshanskii1 orcid ; Mark V. Sapir1
1Vanderbilt University, Nashville, USA
Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1289-1339

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DOI

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 f, there is a QD-group G containing a finitely presented subgroup H whose Dehn function grows faster than f. (3) There exists a group with undecidable conjugacy problem but decidable power conjugacy problem; this group is QD.
DOI : 10.4171/ggd/694
Classification : 20-XX, 03-XX
Mots-clés : Generators and relations in groups, finitely presented groups, the Dehn function of a group, algorithm, S-machine, van Kampen diagram

Alexander Yu. Olshanskii  1   ; Mark V. Sapir  1

1 Vanderbilt University, Nashville, USA 
Alexander Yu. Olshanskii; Mark V. Sapir. Algorithmic problems in groups with quadratic Dehn function. Groups, geometry, and dynamics, Tome 16 (2022) no. 4, pp. 1289-1339. doi: 10.4171/ggd/694
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     title = {Algorithmic problems in groups with quadratic {Dehn} function},
     journal = {Groups, geometry, and dynamics},
     pages = {1289--1339},
     year = {2022},
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     number = {4},
     doi = {10.4171/ggd/694},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/694/}
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