Symmetric groupIn abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions. In particular, the finite symmetric group defined over a finite set of symbols consists of the permutations that can be performed on the symbols. Since there are ( factorial) such permutation operations, the order (number of elements) of the symmetric group is .
PerformanceA performance is an act of staging or presenting a play, concert, or other form of entertainment. It is also defined as the action or process of carrying out or accomplishing an action, task, or function. In the work place, job performance is the hypothesized conception or requirements of a role. There are two types of job performances: contextual and task. Task performance is dependent on cognitive ability, while contextual performance is dependent on personality.
Group dynamicsGroup 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 following the emergence and popularity of new ideas and technologies.
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
Group isomorphismIn abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.
Performance appraisalA performance appraisal, also referred to as a performance review, performance evaluation, (career) development discussion, or employee appraisal, sometimes shortened to "PA", is a periodic and systematic process whereby the job performance of an employee is documented and evaluated. This is done after employees are trained about work and settle into their jobs. Performance appraisals are a part of career development and consist of regular reviews of employee performance within organizations.
HierarchyA hierarchy (from Greek: ἱεραρχία, from hierarkhes, 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science, organizational theory, systems theory, systematic biology, and the social sciences (especially political science).
Group (mathematics)In mathematics, a group is a non-empty set with an operation that satisfies the following constraints: the operation is associative, has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties. For example, the integers with the addition operation is an infinite group, which is generated by a single element called 1 (these properties characterize the integers in a unique way).
Cyclic groupIn group theory, a branch of abstract algebra in pure mathematics, a cyclic group or monogenous group is a group, denoted Cn, that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as an integer power of g in multiplicative notation, or as an integer multiple of g in additive notation.
Performance artPerformance art is an artwork or art exhibition created through actions executed by the artist or other participants. It may be witnessed live or through documentation, spontaneously developed or written, and is traditionally presented to a public in a fine art context in an interdisciplinary mode. Also known as artistic action, it has been developed through the years as a genre of its own in which art is presented live. It had an important and fundamental role in 20th century avant-garde art.
Social groupIn the social sciences, a social group is defined as two or more people who interact with one another, share similar characteristics, and collectively have a sense of unity. Regardless, social groups come in a myriad of sizes and varieties. For example, a society can be viewed as a large social group. The system of behaviors and psychological processes occurring within a social group or between social groups is known as group dynamics.
Hierarchical organizationA hierarchical organization or hierarchical organisation (see spelling differences) is an organizational structure where every entity in the organization, except one, is subordinate to a single other entity. This arrangement is a form of a hierarchy. In an organization, the hierarchy usually consists of a singular/group of power at the top with subsequent levels of power beneath them. This is the dominant mode of organization among large organizations; most corporations, governments, criminal enterprises, and organized religions are hierarchical organizations with different levels of management, power or authority.
Job performanceJob performance assesses whether a person performs a job well. Job performance, studied academically as part of industrial and organizational psychology, also forms a part of human resources management. Performance is an important criterion for organizational outcomes and success. John P. Campbell describes job performance as an individual-level variable, or something a single person does. This differentiates it from more encompassing constructs such as organizational performance or national performance, which are higher-level variables.
Affine groupIn mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into itself. In the case of a Euclidean space (where the associated field of scalars is the real numbers), the affine group consists of those functions from the space to itself such that the image of every line is a line. Over any field, the affine group may be viewed as a matrix group in a natural way. If the associated field of scalars the real or complex field, then the affine group is a Lie group.
Triangle groupIn mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle. The triangle can be an ordinary Euclidean triangle, a triangle on the sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere, or the hyperbolic plane by congruent triangles called Möbius triangles, each one a fundamental domain for the action. Let l, m, n be integers greater than or equal to 2.
Quaternion groupIn group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset of the quaternions under multiplication. It is given by the group presentation where e is the identity element and commutes with the other elements of the group. Another presentation of Q8 is The quaternion group Q8 has the same order as the dihedral group D4, but a different structure, as shown by their Cayley and cycle graphs: In the diagrams for D4, the group elements are marked with their action on a letter F in the defining representation R2.
OrganizationAn organization or organisation (Commonwealth English; see spelling differences), is an entity—such as a company, an institution, or an association—comprising one or more people and having a particular purpose. The word is derived from the Greek word organon, which means tool or instrument, musical instrument, and organ. There are a variety of legal types of organizations, including corporations, governments, non-governmental organizations, political organizations, international organizations, armed forces, charities, not-for-profit corporations, partnerships, cooperatives, and educational institutions, etc.
Performance poetryPerformance poetry is a broad term, encompassing a variety of styles and genres. In brief, it is poetry that is specifically composed for or during a performance before an audience. During the 1980s, the term came into popular usage to describe poetry written or composed for performance rather than print distribution, mostly open to improvisation. The term performance poetry originates from an early press release describing the 1980s performance poet Hedwig Gorski, whose audio recordings achieved success on spoken word radio programs around the world.
Performing artsThe performing arts are arts such as music, dance, and drama which are performed for an audience. They are different from the visual arts, which are the use of paint, canvas or various materials to create physical or static art objects. Performing arts include a range of disciplines which are performed in front of a live audience, including theatre, music, and dance. Theatre, music, dance, object manipulation, and other kinds of performances are present in all human cultures.
Legal personIn law, a legal person is any person or 'thing' (less ambiguously, any legal entity) that can do the things a human person is usually able to do in law – such as enter into contracts, sue and be sued, own property, and so on. The reason for the term "legal person" is that some legal persons are not people: companies and corporations are "persons" legally speaking (they can legally do most of the things an ordinary person can do), but they are not people in a literal sense (human beings).
