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2008, Advanced courses in mathematics, CRM Barcelona, ISBN 9783764388263, xv, 183
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups,... 
Cryptography | Combinatorial group theory | Algorithms
Book
International Journal of Algebra and Computation, ISSN 0218-1967, 09/2017, Volume 27, Issue 6, pp. 633 - 653
In this paper, we study distortion of various well-known embeddings of finitely generated torsion-free nilpotent groups G into unitriangular groups U T n ( ℤ... 
Heisenberg group | unitriangular groups | Nickel's embedding | Nilpotent groups | Jennings' embedding | Mal'cev basis | subgroup distortion | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of symbolic computation, ISSN 0747-7171, 11/2017, Volume 83, pp. 147 - 165
.... In this work we examine Schreier graphs of amalgamated products and HNN extensions. For an amalgamated product G=H⋆AK with [H:A]≥[K:A... 
Generic case complexity | Conjugacy problem | Schreier graph | HNN extension | Amenability | Amalgamated product | Algorithms
Journal Article
2008, Advanced courses in mathematics, CRM Barcelona, ISBN 9783764388270
Web Resource
2008, Advanced courses in mathematics, CRM Barcelona, ISBN 9783764388263
Web Resource
2008, Advanced courses in mathematics, CRM Barcelona, ISBN 9783764388263
Web Resource
Annals of pure and applied logic, ISSN 0168-0072, 11/2011, Volume 162, Issue 11, pp. 916 - 933
In this paper, we give a complete algebraic description of groups elementarily equivalent to the P. Hall completion of a given free nilpotent group of finite... 
Abelian deformation | Elementary equivalence | P. Hall completion | Free nilpotent group | Science & Technology - Other Topics | Physical Sciences | Mathematics | Mathematics, Applied | Logic | Science & Technology
Journal Article
Mathematics of computation, ISSN 0025-5718, 09/2020, Volume 89, Issue 325, pp. 2507 - 2519
In this paper we show that the Diophantine problem in solvable Baumslag-Solitar groups BS(1,k) and in wreath products A \wr \mathbb{Z}, where A is a finitely... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 02/2007, Volume 17, Issue 1, pp. 1 - 26
In this paper we discuss a general approach to positive theories of groups. As an application we get a robust description of positive theories of groups with... 
Positive theory | Groups acting on lambda-trees | Length functions | Infinite words | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of algebra, ISSN 0021-8693, 02/2002, Volume 248, Issue 2, pp. 608 - 668
We re-cast in a more combinatorial and computational form the topological approach of J. Stallings to the study of subgroups of free groups. 
Physical Sciences | Mathematics | Science & Technology
Journal Article
Annals of pure and applied logic, ISSN 0168-0072, 06/2018, Volume 169, Issue 6, pp. 523 - 547
We describe solutions to the problem of elementary classification in the class of group algebras of free groups. We will show that unlike free groups, two... 
Limit group | Group algebra | First-order theory | Science & Technology - Other Topics | Physical Sciences | Mathematics | Mathematics, Applied | Logic | Science & Technology
Journal Article
Journal of pure and applied algebra, ISSN 0022-4049, 2011, Volume 215, Issue 11, pp. 2789 - 2796
We call a group G algorithmically finite if no algorithm can produce an infinite set of pairwise distinct elements of G... 
Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Algorithms
Journal Article
Proceedings of the 2015 ACM on international symposium on symbolic and algebraic computation, 06/2015, Volume 2015-, pp. 141 - 148
...: In this work we examine Schreier graphs of amalgamated products and HNN extensions. For an amalgamated product G=H * A K with [H:A] ≥[K:A... 
hnn extension | generic case complexity | amalgamated product | amenability | schreier graph | conjugacy problem | Generic case complexity | Conjugacy problem | Schreier graph | HNN extension | Amenability | Amalgamated product
Conference Proceeding
Journal of group theory, ISSN 1433-5883, 10/2000, Volume 3, Issue 4, pp. 467 - 479
Journal Article
International Journal of Algebra and Computation, ISSN 0218-1967, 08/2003, Volume 13, Issue 4, pp. 415 - 436
The paper discusses the Andrews–Curtis graph Δk(G,N) of a normal subgroup N in a group G... 
Black box groups | Potential counterexamples | Andrews-Curtis conjecture | Random walks on graphs | Finite groups | Physical Sciences | Mathematics | Science & Technology
Journal Article
Journal of group theory, ISSN 1433-5883, 05/2002, Volume 5, Issue 3, pp. 365 - 381
...] it was shown that if G is any discriminating group, then the universal theory of G coincides with that of its direct square G x G... 
Physical Sciences | Mathematics | Science & Technology
Journal Article
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