{"title":"二次Dehn函数群的算法问题","authors":"A. Olshanskii, M. Sapir","doi":"10.4171/ggd/694","DOIUrl":null,"url":null,"abstract":"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 QDgroups. (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.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":" ","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Algorithmic problems in groups with quadratic Dehn function\",\"authors\":\"A. Olshanskii, M. Sapir\",\"doi\":\"10.4171/ggd/694\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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 QDgroups. (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.\",\"PeriodicalId\":55084,\"journal\":{\"name\":\"Groups Geometry and Dynamics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-12-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Groups Geometry and Dynamics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/ggd/694\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Geometry and Dynamics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/ggd/694","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Algorithmic problems in groups with quadratic Dehn function
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 QDgroups. (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.
期刊介绍:
Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.
Topics covered include:
geometric group theory;
asymptotic group theory;
combinatorial group theory;
probabilities on groups;
computational aspects and complexity;
harmonic and functional analysis on groups, free probability;
ergodic theory of group actions;
cohomology of groups and exotic cohomologies;
groups and low-dimensional topology;
group actions on trees, buildings, rooted trees.