# Group

### Chemistry

A vertical column in the periodic table. All elements in the same group have the same properties. e.g. Group 1 elements all react with water.

### Mathematics

A mathematical system consisting of elements from a set G and a binary operation * such that

- x*y is a member of G whenever x and y are
- (x*y)*z=x*(y*z) for all x, y, and z
- there is an identity element e such that e*x=x*e=e for all x
- each member x in G has an inverse element y such that x*y=y*x=e

**See also: **Periodic Table.