# e-Book On Systems of Equations over Free Partially Commutative Groups (Memoirs of the American Mathematical Society, Number 999) download

## by Montserrat Casals-ruiz,Ilya Kazachkov

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Montserrat Casals-Ruiz; Ilya Kazachkov.

Montserrat Casals-Ruiz; Ilya Kazachkov. Using an analogue of Makanin-Razborov diagrams, the authors give an effective description of the solution set of systems of equations over a partially commutative group (right-angled Artin group) (mathbb{G}). Equivalently, they give a parametrisation of (mathrm{Hom}(G, mathbb{G})), where (G) is a finitely generated group. On Systems of Equations over Free Partially Commutative Groups. Base Product Code Keyword List: memo; MEMO; memo/212; MEMO/212; memo-212; MEMO-212; memo/212/999; MEMO/212/999; memo-212-999; MEMO-212-999.

Duplication prohibited. Please report unauthorized use to [email protected] Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community. On Systems of Equations over Free Partially Commutative Groups resources.

We now focus on equations over partially commutative groups As we have mentioned above, given a system of equations, the two main ques- tions one can ask are whether th. .

We now focus on equations over partially commutative groups,ar R, where R is a subset of the set { i, j 1. r, i j}. This means that the only relations imposed on the generators are commutation of some of the generators. In particular, both free abelian groups and free groups are partially commutative groups

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6 1. INTRODUCTION equations over partially commutative groups is. INTRODUCTION equations over partially commutative groups is decidable, see The fact that partially commutative groups are not CSA, conceptually, shows that this property is not essential for construct- ing Makanin-Razborov diagrams and that the approach developed in this paper opens the possibility for other groups to be taken in consideration: graph prod- ucts of groups, particular types of HNN-extensions (amalgamated products), par- tially e, fully residually. Duplication prohibited.

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Montserrat Casals-Ruiz; Ilya Kazachkov

Montserrat Casals-Ruiz; Ilya Kazachkov.

Memoirs of the American Mathematical Society is a mathematical journal published in six volumes per year, totalling approximately 33 individually bound numbers, by the American Mathematical Society. Usually, a bound number consists of a single paper, .

Notices of the American Mathematical Society is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. The cover regularly features mathematical visualizations.

Authors:Montserrat Casals-Ruiz, Ilya Kazachkov. Submitted on 27 Oct 2008 (v1), last revised 6 Jan 2009 (this version, v2)). Abstract: Version 2: Corrected Section . : instead of lexicographical normal forms we now use a normal form due to V. Diekert and A. Muscholl. Consequent changes made and some misprints corrected.

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