group

In chemistry, a vertical column of elements in the periodic table. Elements in a group have similar physical and chemical properties; for example, the group I elements (the alkali metals: lithium, sodium, potassium, rubidium, caesium, and francium) are all highly reactive metals that form univalent ions. There is a gradation of properties down any group: in group I, melting and boiling points decrease, and density and reactivity increase.

Group 0 consists of the noble gases (rare gases) and group II consists of the alkaline-earth metals. Those elements placed between group II and III are the transition metals and group VII contains the halogens.

group

In mathematics, a finite or infinite set of elements that can be combined by an operation; formally, a group must satisfy certain conditions. For example, the set of all integers (positive or negative whole numbers) forms a group with regard to addition because: (1) addition is associative, that is, the sum of two or more integers is the same regardless of the order in which the integers are added; (2) adding two integers gives another integer; (3) the set includes an identity element 0, which has no effect on any integer to which it is added (for example, 0 + 3 = 3); and (4) each integer has an inverse (for instance, 7 has the inverse −7), such that the sum of an integer and its inverse is 0. Group theory is the study of the properties of groups.

group

In an organization, a number of people who work together. In a formal group, each person has a specific role allocated within the organization (for example, one might be the managing director, another the finance director, and another the sales manager). An informal group is a group of people who join together outside the formal structures of the organization.