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The definition of a group does not require that = for all elements and in . If this additional condition holds, then the operation is said to be commutative, and the group is called an abelian group. It is a common convention that for an abelian group either additive or multiplicative notation may be used, but for a nonabelian group only ...
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.
Sociology. In 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. [1][2] Regardless, social groups come in a myriad of sizes and varieties. For example, a society can be viewed as a large social group.
In sociological terms, groups can fundamentally be distinguished from one another by the extent to which their nature influence individuals and how. [2][3] A primary group, for instance, is a small social group whose members share close, personal, enduring relationships with one another (e.g. family, childhood friend).
Group dynamics is a system of behaviors and psychological processes occurring within a social group (intra group dynamics), or between social groups (inter group 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 ...
Group (stratigraphy), in geology, consisting of formations or rock strata. Cultivar group, in biology, a classification category in the International Code of Nomenclature for Cultivated Plants. Galaxy groups and clusters, in cosmology. Group (firearms), the grouping of shots from a firearm. Language group, a unit of classification within a ...
Collective identity or group identity is a shared sense of belonging to a group. This concept appears within a few social science fields. National identity is a simple example, though myriad groups exist which share a sense of identity. Like many social concepts or phenomena, it is constructed, not empirically defined.
In the of the elements, each column is a group. In chemistry, a group (also known as a family) [1] is a column of elements in the periodic table of the chemical elements. There are 18 numbered groups in the periodic table; the 14 f-block columns, between groups 2 and 3, are not numbered. The elements in a group have similar physical or chemical ...