The unbounded dead-end depth propertie is not a group invariant

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Examples of retracts in a free group that are not the fixed subgroup of any group of automorphisms

Let F be a free group of rank at least three. We show that some retracts of F previously studied by Martino-Ventura are not equal to the fixed subgroup of any group of automorphisms of F. This shows that, in F, there exist subgroups that are equal to the fixed subgroup of some set of endomorphisms but are not equal to the fixed subgroup of any set of automorphisms. Moreover, we determine the Galois monoids of these retracts, where, by the Galois monoid of a subgroup H of F, we mean the monoid consisting of all endomorphisms of F that fix H.

The automorphism group of a free-by-cyclic group in rank 2

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Growth of positive words and lower bounds of the growth rate for Thompson's group (F)p

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Computational explorations in Thompson's group F

Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

On group strategy-proof mechanisms for a many-to-one matching model

For the many-to-one matching model in which firms have substitutable and quota q-separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. In order to prove this result, we also show that under this domain of preferences (which contains the domain of responsive preferences of the college admissions problem) the workers-optimal stable matching is weakly Pareto optimal for the workers and the Blocking Lemma holds as well. We exhibit an example showing that none of these three results remain true if the preferences of firms are substitutable but not quota q-separable.

When does universal peace prevail? Secession and group formation in rent seeking contests and policy conflicts

This paper analyzes secession and group formation in a general model of contest inspired by Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a symmetric coalition structure. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests.

The density of injective endomorphisms of a free group

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Població i família als Andes en el temps de la colònia: parroquia de Toacazo, Cotopaxi, Equador (s. XVIII-XIX )

Estudi elaborat a partir d’una estada a la Facultad Latinoamericana de Ciencias Sociales, durant l’ octubre del 2006. L’estudi de les haciendas creades a partir de la colonització espanyola als territoris americans no pot ser mai complet si no es pot entrar en la vida quotidiana de les persones que les constitueixen. La millor manera de fer-ho és a través d’assolir d’un exhaustiu estudi dels comportaments demogràfics –natalitat, nupcialitat, mortalitat, migracions—i familiars. L’objectiu d’aquest estudi ha estat localitzar una tipologia documental que permeti aquest treball a la parròquia de Toacazo a Cotopaxi (Equador) i, un cop assolida aquesta fita, fotografiar exhaustivament els registres parroquials, altrament dits registre civil antic. El període treballat va des de l’ 1720, any de fundació de la parròquia fins a 1857, any on s’acaba el tributo de indios o règim que regulava les normes de segregació racial de les poblacions.

Organisational structure, communication and group ethics

This paper investigates experimentally how organisational decision processes affect the moral motivations of actors inside a firm that must forego profits to reduce harming a third party. In a "vertical" treatment, one insider unilaterally sets the harm-reduction strategy; the other can only accept or quit. In a "horizontal" treatment, the insiders decide by consensus. Our 2-by-2 design also controls for communication effects. In our data, communication makes vertical firms more ethical; voice appears to mitigate "responsibility-alleviation" in that subordinates with voice feel responsible for what their firms do. Vertical firms are then more ethical than the horizontal firms for which our bargaining data reveal a dynamic form of responsibility-alleviation and our chat data indicate a strong "insider-outsider" effect.

De l'economia a les mentalitats: reforma agrària, desenvolupament rural i identitat ètnica als Andes

Estudi elaborat a partir d’una estada a la Facultad Latinoamericana de Ciencias Sociales, Ecuador, entre setembre i desembre del 2006. El projecte té l'objectiu general d'elaborar una monografia, entre el treball d’arxiu i el de camp, capaç d’exemplificar els processos de consolidació dels sectors dirigents indígenes i de vincular-los amb les transformacions de la societat rural andina contemporània. L’estudi de cas és el d’una organització de segon grau molt representativa (la UNOCANC, parròquia de Toacazo, província de Cotopaxi, Equador), analitzant el que han significat aquest canvis des de la descomposició del règim d’hisenda fins a l’ascens d’una part de l’élite camperola local a les altes instàncies de la CONAIE (Confederación de Nacionalidades Indígenas del Ecuador).

Inter-group conflict and intra-group punishment in an experimental contest game

We study how conflict in a contest game is influenced by rival parties being groups and by group members being able to punish each other. Our main motivation stems from the analysis of socio-political conflict. The relevant theoretical prediction in our setting is that conflict expenditures are independent of group size and independent of whether punishment is available or not. We find, first, that our results contradict the independence of group-size prediction: conflict expenditures of groups are substantially larger than those of individuals, and both are substantially above equilibrium. Towards the end of the experiment material losses in groups are 257% of the predicted level. There is, however, substantial heterogeneity in the investment behaviour of individual group members. Second, allowing group members to punish each other after individual contributions to the contest effort are revealed leads to even larger conflict expenditures. Now material losses are 869% of the equilibrium level and there is much less heterogeneity in individual group members' investments. These results contrast strongly with those from public goods experiments where punishment enhances efficiency and leads to higher material payoffs.