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The composition of the braids σ and τ is written as στ.. The set of all braids on four strands is denoted by .The above composition of braids is indeed a group operation. . The identity element is the braid consisting of four parallel horizontal strands, and the inverse of a braid consists of that braid which "undoes" whatever the first braid did, which is obtained by flipping a diagram ...
Loop braid group; M. Matsumoto's theorem (group theory) S. Spherical braid group
Categorization is a type of cognition involving conceptual differentiation between characteristics of conscious experience, such as objects, events, or ideas.It involves the abstraction and differentiation of aspects of experience by sorting and distinguishing between groupings, through classification or typification [1] [2] on the basis of traits, features, similarities or other criteria that ...
They are closely related with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named after Emil Artin, due to his early work on braid groups in the 1920s to 1940s, [1] and Jacques Tits who developed the theory of a more general class of groups in the ...
Group dynamics is a system of behaviors and psychological processes occurring within a social group (intragroup dynamics), or between social groups (intergroup dynamics). The study of group dynamics can be useful in understanding decision-making behaviour, tracking the spread of diseases in society, creating effective therapy techniques, and ...
It is known that the conjugacy problem is undecidable for many classes of groups. Classes of group presentations for which it is known to be solvable include: free groups (no defining relators) one-relator groups with torsion; braid groups; knot groups; finitely presented conjugacy separable groups
For example, in a threatening scenario, a group of entitative robots can be perceived as more threatening than a single robot, and more threatening a group of robots that are less entitative. [96] In a cohesive context however, perceptions of robot group cohesiveness or entitativity can increase humans' positive perceptions and willingness to ...
The spherical braid group on n strands, denoted or (), is defined as the fundamental group of the configuration space of the sphere: [2] [3] = (()). The spherical braid group has a presentation in terms of generators ,,, with the following relations: [4]