Related papers: Theorie des groupes et psychologie de l'intelligen…

Recent empirical research has shown that links between groups reinforce individuals within groups to adopt cooperative behaviour. Moreover, links between networks may induce cascading failures, competitive percolation, or contribute to…

Research has shown that the maturity of small workgroups from a psychological perspective is intimately connected to team agility. We, therefore, tested if agile team members appreciated group development psychology training. Our results…

There are many Lie groups used in physics, including the Lorentz group of special relativity, the spin groups (relativistic and non-relativistic) and the gauge groups of quantum electrodynamics and the weak and strong nuclear forces.…

In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…

We explore the category of internal categories in the usual category of (right) group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between…

Previous research on organizations often focuses on either the individual, team, or organizational level. There is a lack of multidimensional research on emergent phenomena and interactions between the mechanisms at different levels. This…

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals…

Large language models demonstrate strong problem-solving abilities through reasoning techniques such as chain-of-thought prompting and reflection. However, it remains unclear whether these reasoning capabilities extend to a form of social…

We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

This is a survey concerning the relationship between Lie Groupoids (and their morphisms) and singular foliations in the sense of Sussmann-Stefan (considered from a purely geometrical point of view). We focus on the interaction between the…

A Galois correspondence theorem is proved for the case of inverse semigroups acting orthogonally on commutative rings as a consequence of the Galois correspondence theorem for groupoid actions. To this end, we use a classic result of…

We introduce the existence of a Genus-Type Theory that generalizes classical genus theory by linking fractional ideals of number fields to structures built from their Galois groups and associated Diophantine equations, as formally stated in…

Collectiveness is an important property of many systems--both natural and artificial. By exploiting a large number of individuals, it is often possible to produce effects that go far beyond the capabilities of the smartest individuals, or…

We propose the consistent statistical approach for the quantitative description of simple psychological phenomena using the methods of quantum theory of open systems (QTOS). Taking as the starting point the K. Lewin's psychological field…

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…

Collective Intelligence (CI) is the ability of a group to exhibit greater intelligence than its individual members. Expressed by the common saying that "two minds are better than one," CI has been a topic of interest for social psychology…

We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative…

In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom,…

We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…