A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of closure, associativity, the identity property, and the inverse property.

A group has one operation which satisfies closure, associative property, commutive property, identity, and inverse property. A ring satisfies all properties of a group; it also has a second operation which has closure, associative, and distributive property between these two operations.

Groups – definition and basic properties Next we give two examples of finite groups. For a finite group we denote by the number of elements in . A finite group can be given by its multiplication table (also called the Cayley table). This is a square table of size ;

Physical and Chemical Properties of Group 17 Elements Group 17 Elements: The Halogens The elements in Group 17 are: Fluorine Chlorine Bromine Iodine Astatine These elements are known as halogens. (a) Halogen is a Greek word which means salt-former’.

A group property is something that every group either satisfies or does not satisfy. Group properties must satisfy the condition of isomorphism invariance: if and are two isomorphic groups, they either both have the property or both do not have the property.

## In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely, both from a point of view of representation theory (that is, through the representations of the group) and of computational group theory.

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Physical and Chemical Properties of Group 17 Elements Group 17 Elements: The Halogens The elements in Group 17 are: Fluorine Chlorine Bromine Iodine Astatine These elements are known as halogens. (a) Halogen is a Greek word which means salt-former’.

The members of a group are inter-related to each other. Simply, a gathering of persons cannot form a group. Mutual relations are considered essential for the formation of a social group. 2) Sense of Unity: A sense of unity is essential for every group. Group members are tied by a sense of unity.

The elements in Group 1 are: These elements are known as alkali metals.. Physical Properties of Group 1 Elements. 1. Table shows some properties of Group 1 elements.