Embeddings between partially commutative groups: two counterexamples

In this note we give two examples of partially commutative subgroups of partially commutative groups. Our examples are counterexamples to the Extension Graph Conjecture and to the Weakly Chordal Conjecture of Kim and Koberda, \cite{KK}. On the other hand we extend the class of partially commutative groups for which it is known that the Extension Graph Conjecture holds, to include those with commutation graph containing no induced $C_4$ or $P_3$. In the process, some new embeddings of surface groups into partially commutative groups emerge.Comment: 15 pages, 5 figures; to appear in Journal of Algebr

Teories de primer ordre i els problemes de Tarski

A principis del segle xx, les matemàtiques varen viure una crisi de fonaments coneguda com a Grundlagenkrise der Mathematik. Com a resposta a la necessitat de formalització de les matemàtiques, la lògica matemàtica va experimentar un desenvolupament profund. Aquest desenvolupament va derivar en el naixement de diverses branques de les matemàtiques, entre les quals la teoria de models, que estudia les estructures algebraiques des de la perspectiva de la lògica matemàtica. En aquest article presentem aquest punt de vista, mostrant tant la seva potència com les seves limitacions. Comencem amb l?estudi del cos dels nombres complexos i dels nombres reals revisant els teoremes clàssics de Tarski. Continuem presentant alguns resultats de teoria de grups, com els teoremes de Szmielew sobre la teoria de primer ordre dels grups abelians. Acabem amb un resum de la solució recent dels problemes de Tarski sobre la teoria elemental dels grups lliures.At the beginning of the 20th century, mathematics suffered a foundational crisis, known as the Grundlagenkrise der Mathematik. To answer the need of formalization of mathematics, mathematical logic underwent a profound development. An important outcome of this development was the birth of a new branch of mathematics - Model Theory, which studies algebraic structures from the viewpoint of mathematical logic. In this article we present this approach, its power and its limitations. We begin by reviewing some classical results, such as theorems of A. Tarski on the fields of complex and real numbers. We then present several grouptheoretic results, including results of W. Szmielew on the first-order theory of abelian groups. We finish with a survey of the recent solution of the Tarski problems on the elementary theory of the free group. This article is based on the talk presented by the author to the XIII Meeting of the Catalan Mathematical Society

Al voltant de la innovació

Iniciar un projecte ha estat una oportunitat que ens ha permès obrir-nos a noves possibilitats, plantejar-nos de si l'escola que havíem viscut fins aleshores podia ser diferent. Una qüestió sobre la qual hem anat avançant i volem continuar-ho fent desitjant que el projecte de l'escola no sigui finit i estigui en construcció constant tenint en compte els criteris que ens vam plantejar en el seu moment i que ens van permetre visualitzar el nostre somni quan encara no existia l'escola. Per innovar, necessitem uns referents teòrics, un coneixement profund del context i tenir molt clara la intenció. Les experiències viscudes van ser un punt de partida a partir del qual imaginar altres possibilitats expressades amb nous llenguatges que remeten també a altres significats i amb els quals la comunitat educativa d'El Martinet s'identifica. El compromís d'actualització del projecte ens porta al repte d'oferir en cada moment el millor per a les persones que formem part d'aquest col·lectiu.The start-up of a project was a great opportunity to consider new possibilities, such as whether the school we had known until then could take a different approach. Since then, we have developed these questions thoroughly, always with the willingness to keep advancing with the ongoing school project. To preserve the spirit of learning, we are constantly rethinking the project while always bearing in mind our initial criteria, which allowed us to visualize our school even before it existed. In order to innovate, we need to have theoretical references, a deep knowledge of the context and clear ideas of what we want to do. Our first professional experiences formed a good starting point for dreaming and imagining new opportunities expressed in different languages. This led to new meanings, with which El Martinet identifies itself

On Systems of Equations over Free Partially Commutative Groups

Version 2: Corrected Section 3.3: 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. Using an analogue of Makanin-Razborov diagrams, we give an effective description of the solution set of systems of equations over a partially commutative group (right-angled Artin group) $G$. Equivalently, we give a parametrisation of $Hom(H, G)$, where $H$ is a finitely generated group.Comment: 117 pages, 22 figure

Turvapaikkatutkinnan sanasto

Sanglakhi, Fahima. Turvapaikkatutkinnan sanasto, suomi-persia-englanti. Helsinki, kevät 2015, 37 s., liitteitä 1. Diakonia-ammattikorkeakoulu, Diak Etelä. Asioimistulkkauksen koulutusohjelma, Tulkki (AMK) Kaksikielisten sanastojen puutteen vuoksi, varsinkin kieliparilla suomi-persia, tunsin tarvetta sanaston laatimiseen. Opinnäytetyö on kehittämispainotteinen eli toiminnallinen, jonka tuloksena syntyy uusi tuote. Tämän opinnäytetyön tavoitteena oli tehdä suppea turvapaikkatutkinnan sanasto työkielissä suomi-persia-englanti. Sanasto voi auttaa persian- ja darinkielistä tulkkia valmistautumisessa toimeksiantoihin. Uudistetun asioimistulkkien ammattisäännöstön viidennen kohdan mukaan valmistautumisella tarkoitetaan sitä, että tulkin on perehdyttävä tulkkausaiheeseen ja sen edellyttämään sanastoon ja terminologiaan molemmilla työkielillä. Opinnäytetyön tarkoitus oli helpottaa persian ja darin kielen tulkkien työtä turvapaik-katutkinnassa ja auttaa heitä välittämään viestiä paremmin vaikeista termeistä huolimatta. Opinnäytetyössä aineistona on käytetty Suomen maahanmuuttoviraston kotisivuilla olevaa sanastoa ja pakolaisneuvonnan ja maahanmuuttoviraston yhteistyössä julkistamaa Opas tulkeille -kirjan sanastoa. Sanastoa laadin ensin keräämällä suomenkielisiä termejä ja myöhemmin etsimällä niiden vastineita persiaksi ja englanniksi. Aineisto koostu 157 suomenkielisestä termistä ja niiden vastineista persian ja englannin kielellä. Sanastosta on hyötyä tulkeille, kääntäjille ja opiskelijoille, jotka työskentelevät maahanmuuttoalalla tai ovat muutenkin kiinnostuneita tästä aiheesta. Asiasanat: sanastotyö, persian kieli, suomen kieli, sanastot, maahanmuutto, turvapaikanhakijat, asioimistulkkausSanglakhi, Fahima. Asylum investigation glossary in Finnish, Persian and English. Helsinki, spring 2015, p 37, 1 appendix Diaconia University of Applied Sciences, Diak South. Degree Programme in Community Interpreting, Degree: Interpreter Due to the lack of multilingual glossaries especially in the language pairs of Finnish- Persian, it was necessary to draft a glossary in the field of migration. Aim of this thesis was to make a concise asylum investigation glossary in language pairs of Finnish-Persian-English, which could help Persian and Dari language interpreters in preparing for their assignments. The purpose of this thesis was to facilitate Persian and Dari language interpreters' work in asylum investigation field and help them to forward the messages better, despite the tough terms. The thesis material consisted of glossary of Finnish immigration website and glossary of Interpretation in the asylum processes which were published by collaboration of the Finnish Immigration and Refugee advice centre. I found 157 terms. The glossary was compiled first by collecting Finnish terms and later looking for their equivalents in Persian and English. A glossary is useful for all Persian and Dari language interpreters, translators and students who work and study in the field of immigration or are otherwise interested in this topic