Group (mathematics)

This article is about the basic notions. For advanced topics, see Group theory.

In mathematics, a group is a kind of algebraic structure. A group is a set with an operation. The group's operation shows how to combine any two elements of the group's set to get a third element from the set in a useful way. A familiar example of a group is the set of integers with the addition operation.

Instead of "an element of the group's set", mathematicians usually save words by saying "an element of the group".

Mathematicians use capital letters to stand for groups. They often use G, H, or K.^[1] They also use lower-case letters to stand for group elements. For example, they would say "a is in G" to mean "a is an element of G".

They write group operations with symbols like • or *, or by writing two elements next to each other. So "a • b", "a * b", and "ab" can all mean "the element formed when the group's operation combines a and b".

1. ↑ "Comprehensive List of Algebra Symbols". Math Vault. 2020-03-25. Retrieved 2020-10-12.