Filters








451 Hits in 2.7 sec

Rational subsets of Baumslag-Solitar groups [article]

Michaël Cadilhac, Dmitry Chistikov, Georg Zetzsche
2020 arXiv   pre-print
We consider the rational subset membership problem for Baumslag-Solitar groups.  ...  We show that rational subset membership for Baumslag-Solitar groups BS(1,q) with q> 2 is decidable and PSPACE-complete.  ...  Baumslag-Solitar groups The Baumslag-Solitar groups are the groups BS(p, q) for p, q ∈ N, where BS(p, q) = a, t | ta p t −1 = a q .  ... 
arXiv:2006.11898v1 fatcat:y3q6p66235fwxbqumy6hrafb2q

Rational Subsets of Baumslag-Solitar Groups

Michaël Cadilhac, Dmitry Chistikov, Georg Zetzsche, Emanuela Merelli, Anuj Dawar, Artur Czumaj
2020 International Colloquium on Automata, Languages and Programming  
We consider the rational subset membership problem for Baumslag-Solitar groups.  ...  We show that rational subset membership for Baumslag-Solitar groups BS(1,q) with q ≥ 2 is decidable and PSPACE-complete.  ...  Our characterization is an analog for Baumslag-Solitar groups.  ... 
doi:10.4230/lipics.icalp.2020.116 dblp:conf/icalp/CadilhacCZ20 fatcat:t356o6kjcrdvfivofw76rgw2ea

Automatic structures for subsemigroups of Baumslag–Solitar semigroups

Alan J. Cain
2013 Semigroup Forum  
This paper studies automatic structures for subsemigroups of Baumslag--Solitar semigroups (that is, semigroups presented by < x,y | (yx^m, x^ny) >, where m and n are natural numbers).  ...  An appendix discusses the implications of these results for the theory of Malcev presentations. (A Malcev presentation is a special type of presentation for semigroups embeddable into groups.)  ...  Acknowledgements: The author's doctoral studies, upon which this article is based, were funded by the Carnegie Trust for the Universities of Scotland.  ... 
doi:10.1007/s00233-013-9490-y fatcat:5vlltwucjfayhjvfolwu33sugm

Tiling Problems on Baumslag-Solitar groups

Nathalie Aubrun, Jarkko Kari
2013 Electronic Proceedings in Theoretical Computer Science  
A consequence of our construction is the existence of an arecursive tile set on Baumslag-Solitar groups.  ...  We exhibit a weakly aperiodic tile set for Baumslag-Solitar groups, and prove that the domino problem is undecidable on these groups.  ...  Acknowledgement This work has been supported by the Academy of Finland Grant 131558 and by ANR project SubTile.  ... 
doi:10.4204/eptcs.128.12 fatcat:7eesubdlvzhzlpnajs3svtrlye

Baumslag-Solitar groups, relative profinite completions and measure equivalence rigidity [article]

Cyril Houdayer, Sven Raum
2015 arXiv   pre-print
We also obtain a complete classification of direct products of relative profinite completions of Baumslag-Solitar groups, continuing recent work of Elder and Willis.  ...  This generalises some of the results obtained by Kida and moreover provides new measure equivalence rigidity phenomena for Baumslag-Solitar groups.  ...  The relative profinite completion of Baumslag-Solitar groups In this section, we prove several results on the structure of relative profinite completions of Baumslag-Solitar groups and their products.  ... 
arXiv:1308.5855v4 fatcat:3xax4we3sbhnfgdwqiiy2rw45e

A Logspace Solution to the Word and Conjugacy problem of Generalized Baumslag-Solitar Groups [article]

Armin Weiß
2016 arXiv   pre-print
Baumslag-Solitar groups were introduced in 1962 by Baumslag and Solitar as examples for finitely presented non-Hopfian two-generator groups.  ...  Since then, they served as examples for a wide range of purposes. As Baumslag-Solitar groups are HNN extensions, there is a natural generalization in terms of graph of groups.  ...  Many thanks goes to my thesis advisor, Volker Diekert, as well as to Jonathan Kausch with whom I had so many inspiring conversations about complexity and Baumslag-Solitar groups.  ... 
arXiv:1602.02445v2 fatcat:ara7br57ifaqzlbbo6htdr7q6a

Page 886 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
{In Corollary5 the author seems to define an “essential Baumslag-Solitar quotient” as a “quotient group of B(n,m) = (a,b| a~'b"a = b"), m>n>O”.  ...  The author probably means by “an essential Baumslag-Solitar quo- tient” a quotient of B(n,m) where the image of 6 has infinite order.}  ... 

Algorithmic Problems in Group Theory (Dagstuhl Seminar 19131)

Volker Diekert, Olga Kharlampovich, Markus Lohrey, Alexei Myasnikov, Michael Wagner
2019 Dagstuhl Reports  
On the other hand, concepts from these computer science fields as well as efficient algorithms, cryptography, and data compression led to the formulation of new questions in group theory.  ...  This report documents the material presented during the course of the seminar.  ...  Baumslag-Solitar groups.  ... 
doi:10.4230/dagrep.9.3.83 dblp:journals/dagstuhl-reports/DiekertKLM19 fatcat:7b3cwlpo6zdsxfzhiznob5cvsi

Limits of Baumslag-Solitar groups [article]

Luc Guyot, Yves Stalder
2010 arXiv   pre-print
We give a parametrization by m-adic integers of the limits of Baumslag-Solitar groups (marked with a canonical set of generators).  ...  We show that all such limits are extensions of a free group by a lamplighter group and all but possibly one are not finitely presented.  ...  We also thank our advisors, Goulnara Arzhantseva and Alain Valette, for their valuable comments on previous versions of this article.  ... 
arXiv:math/0507236v7 fatcat:3a3i5u376zdv7fo7b6v76djzsi

The large scale geometry of some metabelian groups [article]

J. Taback, K. Whyte
2003 arXiv   pre-print
We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogues of the solvable Baumslag-Solitar groups BS(1,n).  ...  We study the large scale geometry of the upper triangular subgroup of PSL(2,Z[1/n]), which arises naturally in a geometric context.  ...  Rigidity of Baumslag-Solitar groups.  ... 
arXiv:math/0301178v1 fatcat:ykauzo3ywbf4rebv3nwekvy65u

Page 7335 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
For the Baumslag-Solitar groups of type G, = (a,t| ta” = at), although the set of all geodesic words is not regular, rational growth can be deduced from the regularity of a particular subset of geodesics  ...  Finally, in Section 6, results are listed which prove the rational growth of the braid groups and certain Baumslag-Solitar groups.  ... 

The large scale geometry of some metabelian groups

Jennifer Taback, Kevin Whyte
2004 The Michigan mathematical journal  
We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogues of the solvable Baumslag-Solitar groups BS(1, n).  ...  We study the large scale geometry of the upper triangular subgroup of P SL2(Z[ 1 n ]), which arises naturally in a geometric context.  ...  Rigidity of Baumslag-Solitar groups.  ... 
doi:10.1307/mmj/1080837744 fatcat:xrmys2c4zfbnfpgafbpqg5owcu

Decidability of membership problems for flat rational subsets of GL(2, Q) and singular matrices

Volker Diekert, Igor Potapov, Pavel Semukhin
2020 Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation  
the Baumslag-Solitar group BS(1, ), with ≥ 2, of infinite index.  ...  Namely, we introduce a notion of flat rational sets: if is a monoid and ≤ is its submonoid, then flat rational sets of relative to are finite unions of the form 0 1 1 · · · where all s are rational subsets  ...  If such a group is not isomorphic to GL(2, Z) × Z , then our dichotomy states that it contains a Baumslag-Solitar group BS (1, ) for ≥ 2.  ... 
doi:10.1145/3373207.3404038 dblp:conf/issac/DiekertPS20 fatcat:65rgw7q4rjdmrmjbvawecvsczq

Growth functions for some nonautomatic Baumslag-Solitar groups

Marcus Brazil
1994 Transactions of the American Mathematical Society  
In this paper we use finite state automata to investigate the growth function for the Baumslag-Solitar group of the form {a, b | a~lba = a2) based on an analysis of its combinatorial and geometric structure  ...  The rationality of the growth function of this group is particularly interesting as it is known not to be synchronously automatic.  ...  The class of groups with presentation (a, 11 taP = aqt), p, q e N, are often referred to as the Baumslag-Solitar groups (after Baumslag and Solitar's classification of when these group groups are Hopfian  ... 
doi:10.1090/s0002-9947-1994-1169911-8 fatcat:fbhkdungqjfl7nxexu3er7notu

Growth Functions for Some Nonautomatic Baumslag-Solitar Groups

Marcus Brazil
1994 Transactions of the American Mathematical Society  
In this paper we use finite state automata to investigate the growth function for the Baumslag-Solitar group of the form {a, b | a~lba = a2) based on an analysis of its combinatorial and geometric structure  ...  The rationality of the growth function of this group is particularly interesting as it is known not to be synchronously automatic.  ...  The class of groups with presentation (a, 11 taP = aqt), p, q e N, are often referred to as the Baumslag-Solitar groups (after Baumslag and Solitar's classification of when these group groups are Hopfian  ... 
doi:10.2307/2154687 fatcat:22bcsih4nffmzcco4qroqbuity
« Previous Showing results 1 — 15 out of 451 results