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Journal of Algebra, ISSN 0021-8693, 04/2016, Volume 452, pp. 17 - 41
We study the (virtual) indicability of the automorphism group Aut(AΓ) of the right-angled Artin group AΓ associated to a simplicial graph Γ. First, we identify... 
Automorphism | Virtually indicable | Property T | Right-angled Artin group | MATHEMATICS
Journal Article
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 2019, Volume 150, Issue 2, pp. 871 - 895
We present a new test for studying asphericity and diagrammatic reducibility of group presentations. Our test can be applied to prove diagrammatic reducibility... 
DR presentations | Adian presentations | Asphericity | weight test | locally indicable groups | labelled oriented trees | MATHEMATICS, APPLIED | COMPLEXES | EQUATIONS | COVERINGS | 2-COMPLEXES | MATHEMATICS | SYSTEMS
Journal Article
Journal Article
Israel Journal of Mathematics, ISSN 0021-2172, 8/2018, Volume 227, Issue 1, pp. 379 - 396
We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only... 
Algebra | Analysis | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | Group Theory and Generalizations | Applications of Mathematics | MATHEMATICS | LOCALLY INDICABLE GROUP | Research | Isomorphisms (Mathematics) | Mathematical research | Group theory | Geometric Topology
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 326, Issue 1, pp. 4 - 33
Recently Dicks–Linnell determined the L 2 -Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that... 
[formula omitted]-Betti number | Surface-plus-one-relation group | L2-Betti number | MATHEMATICS | THEOREM | FREE-PRODUCTS | RING | LOCALLY INDICABLE GROUPS | EQUATIONS | L-2-Betti number
Journal Article
Journal Article
Groups, Geometry, and Dynamics, ISSN 1661-7207, 2014, Volume 8, Issue 2, pp. 467 - 478
We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show... 
Locally invariant order | Right-orderable group | Locally indicable | Amenable group | Recurrent order | Left-orderable group | Left-invariant order | MATHEMATICS | locally indicable | right-orderable group | left-orderable group | left-invariant order | recurrent order | amenable group
Journal Article
Journal of Topology and Analysis, ISSN 1793-5253, 2014, Volume 6, Issue 4, pp. 557 - 571
In recent decades, many remarkable papers have appeared which are devoted to the study of finitely generated subgroups of Diff(+)([0, 1]) (see [ 8, 15, 16,... 
discrete subgroups | Diffeomorphism groups of 1-manifolds | dense subgroups | DIFFEOMORPHISMS | INTERVAL | ONE-MANIFOLDS | PIECEWISE-LINEAR HOMEOMORPHISMS | CIRCLE | GROUP-F | MATHEMATICS | SOLVABLE-GROUPS | LIE-GROUPS | LOCALLY INDICABLE GROUP | REAL
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 08/2013, Volume 23, Issue 5, pp. 1207 - 1223
In this paper, we generalize Magnus' Freiheitssatz and solution to the word problem for one-relator groups by considering one-relator quotients of certain... 
word-problem | graph groups | locally indicable groups | Freiheitssatz | right-angled Artin groups | one-relator quotient | Graph products | MATHEMATICS | EQUATIONS | Graphs | Mathematical models | Algebra | Computation | Quotients | Mathematics - Group Theory
Journal Article
ALGEBRAIC AND GEOMETRIC TOPOLOGY, ISSN 1472-2739, 2006, Volume 6, Issue 5, pp. 2509 - 2518
Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real... 
MATHEMATICS
Journal Article
MATHEMATISCHE ZEITSCHRIFT, ISSN 0025-5874, 08/2017, Volume 286, Issue 3-4, pp. 919 - 949
We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts... 
DIFFEOMORPHISMS | MATHEMATICS | Solvable groups | HOMEOMORPHISMS | LOCALLY INDICABLE GROUP | Actions on 1-manifolds | BAUMSLAG-SOLITAR GROUPS | CLASSIFICATION | Rigidity | Hyperbolicity | C-1 diffeomorphisms | CIRCLE | Mathematics
Journal Article
by Shi, EH and Zhou, LZ
GROUPS GEOMETRY AND DYNAMICS, ISSN 1661-7207, 2019, Volume 13, Issue 1, pp. 293 - 307
For every group G, we show that either G has a topologically transitive action on the line R by orientation-preserving homeomorphisms, or every... 
MATHEMATICS | Baumslag-Solitar group | solvable group | Topological transitivity | indicable group | orderable group
Journal Article
Forum Mathematicum, ISSN 0933-7741, 05/2020, Volume 32, Issue 3, pp. 739 - 772
Let be a division ring of fractions of a crossed product , where is a skew field and is a group with Conradian left-order . For we introduce the notion of... 
16W60 | 12E15 | 16S34 | 16S85 | division ring of fractions | group ring | formal power series | Conradian left-order | 20F60 | locally indicable group | ordered group | Crossed product | 16S35 | Hughes-free | MATHEMATICS | MATHEMATICS, APPLIED | Vector space | Power series
Journal Article
Lobachevskii Journal of Mathematics, ISSN 1995-0802, 3/2018, Volume 39, Issue 2, pp. 218 - 223
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2010, Volume 60, Issue 5, pp. 1685 - 1740
We develop dynamical methods for studying left-orderable groups as well as the spaces of orderings associated to them. We give new and elementary proofs of... 
Orderable groups | Conradian ordering | Actions on the line | 3-MANIFOLD GROUPS | INTERVAL | BRAIDS | SPACES | actions on the line | CIRCLE | MATHEMATICS | ORDERINGS | LOCALLY INDICABLE GROUP | LINE | ORDERED-GROUPS | AMENABLE-GROUPS
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 2010, Volume 10, Issue 4, pp. 2409 - 2418
We prove that the free group F-2 admits a faithful discrete representation into Diff(+)(1)[0, 1]. We also prove that F-2 admits a faithful discrete... 
DIFFEOMORPHISMS | INTERVAL | MATHEMATICS | HOMEOMORPHISMS | LOCALLY INDICABLE GROUP | ONE-MANIFOLDS | CIRCLE
Journal Article
GEOMETRY & TOPOLOGY, ISSN 1364-0380, 2010, Volume 14, Issue 1, pp. 573 - 584
According to Thurston's stability theorem, every group of C-1 diffeomorphisms of the closed interval is locally indicable (that is, every finitely generated... 
MATHEMATICS | SUBGROUPS | CIRCLE
Journal Article
Communications in Algebra, ISSN 0092-7872, 2004, Volume 32, Issue 3, pp. 1127 - 1149
Journal Article
Communications in Algebra, ISSN 0092-7872, 12/2004, Volume 32, Issue 3, pp. 1127 - 1149
Let G be a locally indicable group, K a division ring, and KG a crossed-product group ring. In 1961, Ian Hughes proved that, up to KG-isomorphism, at most one... 
Locally indicable group | Division ring of fractions | Hughes-free | MATHEMATICS | locally indicable group | division ring of fractions | ALGEBRAS
Journal Article
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