Log in

Relevant bibliographies by topics / Combinatorial group theory. Free groups. Equations

Contents

Journal articles
Books
Book chapters
Conference papers

Academic literature on the topic 'Combinatorial group theory. Free groups. Equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Combinatorial group theory. Free groups. Equations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Combinatorial group theory. Free groups. Equations"

1

Solomon, Reed. "Ordered Groups: A Case Study in Reverse Mathematics." Bulletin of Symbolic Logic 5, no. 1 (1999): 45–58. http://dx.doi.org/10.2307/421140.

Full text

Abstract:

The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is best explained by an exam

APA, Harvard, Vancouver, ISO, and other styles

2

MANTUROV, O. V., and V. O. MANTUROV. "FREE KNOTS AND GROUPS." Journal of Knot Theory and Its Ramifications 19, no. 02 (2010): 181–86. http://dx.doi.org/10.1142/s0218216510007826.

Full text

Abstract:

Free knots are a simplification of virtual knots obtained by forgetting arrow/sign information at classical crossings. First non-trivial examples of free knots were constructed recently by the second named author. By using parity considerations, we construct invariants of free knots valued in certain groups. These groups have a simple combinatorial description, the first one being the infinite dihedral group.

APA, Harvard, Vancouver, ISO, and other styles

3

DELGADO, MANUEL, STUART MARGOLIS, and BENJAMIN STEINBERG. "COMBINATORIAL GROUP THEORY, INVERSE MONOIDS, AUTOMATA, AND GLOBAL SEMIGROUP THEORY." International Journal of Algebra and Computation 12, no. 01n02 (2002): 179–211. http://dx.doi.org/10.1142/s0218196702000924.

Full text

Abstract:

This paper explores various connections between combinatorial group theory, semigroup theory, and formal language theory. Let G = <A|R> be a group presentation and ℬA, R its standard 2-complex. Suppose X is a 2-complex with a morphism to ℬA, R which restricts to an immersion on the 1-skeleton. Then we associate an inverse monoid to X which algebraically encodes topological properties of the morphism. Applications are given to separability properties of groups. We also associate an inverse monoid M(A, R) to the presentation <A|R> with the property that pointed subgraphs of covers of

APA, Harvard, Vancouver, ISO, and other styles

4

Guo, Xiao Qiang, and Zheng Jun He. "The History, Classes and Presentations of Groups." Advanced Materials Research 430-432 (January 2012): 834–37. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.834.

Full text

Abstract:

First we introduce the history of group theory. Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. Secondly, we give the main classes of groups: permutation groups, matrix groups, transformation groups, abstract groups and topological and algebraic groups. Finally, we give two different presentations of a group: combinatorial group theory and geometric group theory.

APA, Harvard, Vancouver, ISO, and other styles

5

Bibi, Mairaj, and Martin Edjvet. "Solving equations of length seven over torsion-free groups." Journal of Group Theory 21, no. 1 (2018): 147–64. http://dx.doi.org/10.1515/jgth-2017-0032.

Full text

Abstract:

AbstractPrishchepov [16] proved that all equations of length at most six over torsion-free groups are solvable. A different proof was given by Ivanov and Klyachko in [12]. This supports the conjecture stated by Levin [15] that any equation over a torsion-free group is solvable. Here it is shown that all equations of length seven over torsion-free groups are solvable.

APA, Harvard, Vancouver, ISO, and other styles

6

Diekert, Volker, Olga Kharlampovich, and Atefeh Mohajeri Moghaddam. "SLP compression for solutions of equations with constraints in free and hyperbolic groups." International Journal of Algebra and Computation 25, no. 01n02 (2015): 81–111. http://dx.doi.org/10.1142/s0218196715400056.

Full text

Abstract:

The paper is a part of an ongoing program which aims to show that the problem of satisfiability of a system of equations in a free group (hyperbolic or even toral relatively hyperbolic group) is NP-complete. For that, we study compression of solutions with straight-line programs (SLPs) as suggested originally by Plandowski and Rytter in the context of a single word equation. We review some basic results on SLPs and give full proofs in order to keep this fundamental part of the program self-contained. Next we study systems of equations with constraints in free groups and more generally in free

APA, Harvard, Vancouver, ISO, and other styles

7

Satoh, Takao. "On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (2021): 338–63. http://dx.doi.org/10.1017/s0013091521000171.

Full text

Abstract:

AbstractIn this paper, we study the structure of the rational cohomology groups of the IA-automorphism group $\mathrm {IA}_3$ of the free group of rank three by using combinatorial group theory and representation theory. In particular, we detect a nontrivial irreducible component in the second cohomology group of $\mathrm {IA}_3$, which is not contained in the image of the cup product map of the first cohomology groups. We also show that the triple cup product of the first cohomology groups is trivial. As a corollary, we obtain that the fourth term of the lower central series of $\mathrm {IA}_

APA, Harvard, Vancouver, ISO, and other styles

8

Manturov, Vassily Olegovich. "Reidemeister moves and groups." Journal of Knot Theory and Its Ramifications 24, no. 10 (2015): 1540006. http://dx.doi.org/10.1142/s0218216515400064.

Full text

Abstract:

Recently, the author discovered an interesting class of knot-like objects called free knots. These purely combinatorial objects are equivalence classes of Gauss diagrams modulo Reidemeister moves (the same notion in the language of words was introduced by Turaev [Topology of words, Proc. Lond. Math. Soc.95(3) (2007) 360–412], who thought all free knots to be trivial). As it turned out, these new objects are highly nontrivial, see [V. O. Manturov, Parity in knot theory, Mat. Sb.201(5) (2010) 65–110], and even admit nontrivial cobordism classes [V. O. Manturov, Parity and cobordisms of free knot

APA, Harvard, Vancouver, ISO, and other styles

9

Shelah, Saharon. "Pcf and abelian groups." form 25, no. 5 (2013): 967–1038. http://dx.doi.org/10.1515/forum-2013-0119.

Full text

Abstract:

Abstract. We deal with some pcf (possible cofinality theory) investigations mostly motivated by questions in abelian group theory. We concentrate on applications to test problems but we expect the combinatorics will have reasonably wide applications. The main test problem is the “trivial dual conjecture” which says that there is a quite free abelian group with trivial dual. The “quite free” stands for “-free” for a suitable cardinal , the first open case is . We almost always answer it positively, that is, prove the existence of -free abelian groups with trivial dual, i.e., with no non-trivial

APA, Harvard, Vancouver, ISO, and other styles

10

FARAMARZI SALLES, ASADOLLAH, and HASSAN KHOSRAVI. "A COMBINATORIAL PROPERTY OF BURNSIDE VARIETY OF GROUPS OF FINITE EXPONENT." Journal of Algebra and Its Applications 08, no. 06 (2009): 845–53. http://dx.doi.org/10.1142/s0219498809003680.

Full text

Abstract:

Let w be a word in the free group on the set {x1, …, xn} and let [Formula: see text] be the variety of groups defined by the law w = 1. Define [Formula: see text], to be the class of all groups G in which for all infinite subsets Y1, …, Yn, there exist yi ∈ Yi such that w(y1, …, yn) = 1 and define [Formula: see text] (respectively [Formula: see text]) to be the class of all groups G in which for all infinite subset Y (respectively for all m-element subset Y) there exist n distinct elements y1, …, yn ∈ Y, such that w(y1, …, yn) = 1. In this paper we prove that [Formula: see text] and [Formula:

APA, Harvard, Vancouver, ISO, and other styles

More sources

Books on the topic "Combinatorial group theory. Free groups. Equations"

1

Flannery, D. L. (Dane Laurence), 1965-, ed. Algebraic design theory. American Mathematical Society, 2011.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

Jacques, Sauloy, and Singer Michael F. 1950-, eds. Galois theories of linear difference equations: An introduction. American Mathematical Society, 2016.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

I, Arnolʹd V. Experimental mathematics. MSRI Mathematical Sciences Research Institute, 2015.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

4

Shpilrain, Vladimir, Alexander Mikhalev, and Jie-tai Yu. Combinatorial Methods: Free Groups, Polynomials, and Free Algebras. Springer, 2014.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

5

Combinatorial Methods: Free Groups, Polynomials, and Free Algebras (CMS Books in Mathematics). Springer, 2003.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

6

Exponential Genus Problems in One-relator Products of Groups (Memoirs of the American Mathematical Society). American Mathematical Society, 2007.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Combinatorial group theory. Free groups. Equations"

1

Kharlampovich, Olga, and Alexei G. Myasnikov. "Equations and Fully Residually Free Groups." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Morar, Pavel V., and Artem N. Shevlyakov. "Algebraic Geometry over the Additive Monoid of Natural Numbers: Systems of Coefficient Free Equations." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_11.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Lyndon, Roger C., and Paul E. Schupp. "Free Groups and Their Subgroups." In Combinatorial Group Theory. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-61896-3_1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Weidmann, Richard. "Generating Tuples of Virtually Free Groups." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_13.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Frenkel, Elizaveta, Alexei G. Myasnikov, and Vladimir N. Remeslennikov. "Regular Sets and Counting in Free Groups." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Hock, Martin, and Boaz Tsaban. "Solving Random Equations in Garside Groups Using Length Functions." In Combinatorial and Geometric Group Theory. Birkhäuser Basel, 2010. http://dx.doi.org/10.1007/978-3-7643-9911-5_6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Collins, Donald J. "PEAK REDUCTION AND AUTOMORPHISMS OF FREE GROUPS AND FREE PRODUCTS." In Combinatorial Group Theory and Topology. (AM-111), edited by S. M. Gersten and John R. Stallings. Princeton University Press, 1987. http://dx.doi.org/10.1515/9781400882083-006.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Stallings, John R. "GRAPHICAL THEORY OF AUTOMORPHISMS OF FREE GROUPS." In Combinatorial Group Theory and Topology. (AM-111), edited by S. M. Gersten and John R. Stallings. Princeton University Press, 1987. http://dx.doi.org/10.1515/9781400882083-005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Gersten, S. M. "NONSINGULAR EQUATIONS OF SMALL WEIGHT OVER GROUPS." In Combinatorial Group Theory and Topology. (AM-111), edited by S. M. Gersten and John R. Stallings. Princeton University Press, 1987. http://dx.doi.org/10.1515/9781400882083-007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Baumslag, Gilbert. "Free groups, the calculus of presentations and the method of Reidemeister and Schreier." In Topics in Combinatorial Group Theory. Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8587-4_3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Combinatorial group theory. Free groups. Equations"

1

Lynett, Patrick, Philip L. F. Liu, Hwung-Hweng Hwung, and Wen-Son Ching. "Multi-Layer Modeling of Wave Groups From Deep to Shallow Water." In ASME 2003 22nd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2003. http://dx.doi.org/10.1115/omae2003-37087.

Full text

Abstract:

A set of model equations for water wave propagation is derived by piecewise integration of the primitive equations of motion through N arbitrary layers. Within each layer, an independent velocity profile is determined. With N separate velocity profiles, matched at the interfaces of the layers, the resulting set of equations have N+1 free parameters, allowing for an optimization with known analytical properties of water waves. The optimized two-layer model equations show good linear wave characteristics up to kh ≈8, while the second-order nonlinear behavior is well captured to kh ≈6. The three-

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!