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Advances in Mathematics, ISSN 0001-8708, 12/2017, Volume 321, pp. 326 - 390
In this paper, we prove that the group of homotopy automorphisms of the profinite completion of the operad of little 2-disks is isomorphic to the profinite... 
Grothendieck–Teichmüller group | Little disk operad | Profinite completion | MATHEMATICS | IND-CATEGORIES | SPACES | Grothendieck-Teichmuller group | HOMOTOPY-THEORY
Journal Article
Houston Journal of Mathematics, ISSN 0362-1588, 2018, Volume 44, Issue 3, pp. 753 - 767
We provide a concrete description of the profinite completion of arbitrary MV-algebras in terms of their finite simple quotients, a description that... 
Profinite MV-algebra | Semisimple MV-algebra | Separating MV-algebra | Rank of maximal ideal | Profinite completion | MATHEMATICS | profinite completion | separating MV-algebra | rank of maximal ideal | profinite MV-algebra
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 12/2018, Volume 143, pp. 7 - 16
This article describes an invariant random walk on the profinite completion of a finitely generated group which is also residually finite. The infinitesimal... 
Profinite groups | Random walks | Profinite completions | STATISTICS & PROBABILITY | MARKOV-PROCESSES
Journal Article
Journal of Topology and Analysis, ISSN 1793-5253, 09/2018, Volume 10, Issue 3, pp. 563 - 584
We construct metric spaces that do not have property A yet are coarsely embeddable into the Hilbert space. Our examples are so-called warped cones, which were... 
profinite completion | Warped cone | amenable group | property A | Haagerup property | coarse embedding | ADMIT | EMBEDDABILITY | BAUM-CONNES CONJECTURE | BOX SPACES | PROPERTY | MATHEMATICS | PRODUCTS | HILBERT-SPACE
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 02/2016, Volume 109, pp. 130 - 138
In this note we describe a continuous time random walk on the profinite completion Ẑ of the integers Z, which is a profinite group. The infinitesimal... 
Profinite group | Random walks | Profinite completion | Secondary | Primary | STATISTICS & PROBABILITY
Journal Article
Journal Article
Algebraic and Geometric Topology, ISSN 1472-2747, 08/2018, Volume 18, Issue 5, pp. 3013 - 3030
We study several properties of the completed group ring (Z) over cap [t((Z) over cap)] and the completed Alexander modules of knots. Then we prove that if the... 
Knot | Profinite group ring | Branched covering | Profinite completion | MATHEMATICS | REPRESENTATIONS | RIGIDITY
Journal Article
ISRAEL JOURNAL OF MATHEMATICS, ISSN 0021-2172, 06/2014, Volume 200, Issue 1, pp. 1 - 17
We consider some sufficient conditions for the pro-p completion of an orientable Poincar, duality group of dimension n >= 3 to be a virtually pro-p Poincar,... 
MATHEMATICS | COHOMOLOGY | FINITENESS CONDITIONS | PROFINITE
Journal Article
Monatshefte fur Mathematik, ISSN 0026-9255, 10/2014, Volume 175, Issue 3, pp. 367 - 384
Let C be a class of finite groups. We study some sufficient conditions for the pro-C completion of an orientable PD3-pair over Z to be an orientable profinite... 
pro-C completion | pair | p-good group | MATHEMATICS | P GROUPS | PD3-pair | PROFINITE | POINCARE-DUALITY GROUPS
Journal Article
Algebra Universalis, ISSN 0002-5240, 2009, Volume 61, Issue 3-4, pp. 449 - 453
Following Bezhanishvili and Vosmaer, we confirm a conjecture of Yde Venema by piecing together results from various authors. Specifically, we show that if A is... 
MacNeille completion | Modal algebra | Profinite completion | MATHEMATICS | LATTICE EXPANSIONS | profinite completion | CANONICAL EXTENSIONS | modal algebra | Heat shock proteins | Mathematics - Logic
Journal Article
Groups, Geometry, and Dynamics, ISSN 1661-7207, 2012, Volume 6, Issue 2, pp. 221 - 229
We show that property (T) is not profinite, that is, we construct two finitely generated residually finite groups which have isomorphic profinite completions,... 
Profinite groups | Kazhdan's property (T) | Profinite properties | Arithmetic groups | arithmetic groups | MATHEMATICS | profinite properties
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 05/2016, Volume 26, Issue 3, pp. 551 - 564
We study when an abstract finitely presented group G of cohomological dimension cd ( G ) = 2 has pro- p completion Ĝ p of cohomological dimension cd ( Ĝ p ) ≤... 
cohomological dimension | Pro-p completion | limit group | LIMIT GROUPS | MATHEMATICS | ELEMENTARY THEORY | PROFINITE | POINCARE-DUALITY GROUPS | RESIDUALLY FREE GROUPS | GEOMETRY
Journal Article
Revista Matematica Iberoamericana, ISSN 0213-2230, 2014, Volume 30, Issue 1, pp. 165 - 190
Let R be a finitely generated virtually free group (a finite extension of a free group) and let H be a finitely generated subgroup of R. Denote by R the... 
Profinite groups | Residually finite groups | Normalizer | Conjugacy separability | MATHEMATICS | normalizer | profinite groups | conjugacy separability | FREE-PRODUCTS
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 08/2012, Volume 22, Issue 5, pp. 1250045 - 1250026
In this paper we prove that the profinite completion $\mathcal{\widehat G}$ of the Grigorchuk group $\mathcal{G}$ is not finitely presented as a profinite... 
MATHEMATICS | profinite completion | PRESENTATIONS | BRANCH GROUPS | Grigorchuk group | Algebra | Multipliers | Computation | Mathematical analysis | Quotients | Mathematics - Group Theory
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 326, Issue 1, pp. 59 - 73
We consider pairs of finitely presented, residually finite groups P ↪ Γ for which the induced map of profinite completions P ˆ → Γ ˆ is an isomorphism. We... 
Profinite groups | Isomorphism problem | Conjugacy problem | MATHEMATICS | REPRESENTATIONS | PRODUCTS | SUBGROUPS | CONJUGACY | Algorithms
Journal Article
Order, ISSN 0167-8094, 7/2014, Volume 31, Issue 2, pp. 189 - 216
Canonical extensions of (bounded) lattices have been extensively studied, and the basic existence and uniqueness theorems for these have been extended to... 
Geometry | Completion | Discrete Mathematics in Computer Science | Convex and Discrete Geometry | Semilattice | Primary: 06A12 | Mathematics | Theory of Computation | Secondary: 06B23 | Lattice | Profinite completion | Canonical extension | MATHEMATICS
Journal Article
Annals of Physics, ISSN 0003-4916, 01/2020, Volume 412, p. 168014
Haah codes represent a singularly interesting gapped Hamiltonian schema that has resisted a natural generalization, although recent work shows that the closely... 
3-manifold | Haah code | Profinite completion | PHYSICS, MULTIDISCIPLINARY
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 8, pp. 2111 - 2140
Two groups are said to have the same nilpotent genus if they have the same nilpotent quotients. We answer four questions of Baumslag concerning nilpotent... 
FINITENESS PROPERTIES | MATHEMATICS | REPRESENTATIONS | PRODUCTS | SIMPLICITY | ALGEBRA | SUBGROUPS | HOMOLOGY | PROFINITE COMPLETIONS | Homology | Quotients | Mathematical analysis | Formulas (mathematics) | Subgroups | Mathematics - Group Theory
Journal Article
Algebra universalis, ISSN 0002-5240, 11/2011, Volume 66, Issue 3, pp. 205 - 241
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 02/2014, Volume 24, Issue 1, pp. 33 - 46
We construct an uncountable family of 3-generated residually finite just-infinite groups with isomorphic profinite completions. We also show that word growth... 
genus of a group | Profinite completion | iterated monodromy groups | MATHEMATICS | FINITE QUOTIENTS | SET | GENERATED NILPOTENT GROUPS | REPRESENTATIONS | GROTHENDIECK | GROWTH | Construction | Algebra | Computation | Mathematical analysis
Journal Article
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