subgroup

In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.

~10 min read

Article

15 sections

Contents

Subgroup tests
Basic properties of subgroups
Cosets and Lagrange's theorem
Example: Subgroups of S<sub>4</sub>{{anchor|Subgroups of S4}}
24 elements
12 elements
8 elements
6 elements
4 elements
3 elements
2 elements
1 element
Other examples
Notes
References

In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G.

Formally, given a group under a binary operation ∗, a subset of is called a subgroup of if also forms a group under the operation ∗. More precisely, is a subgroup of if the restriction of ∗ to is a group operation on . This is often denoted , read as " is a subgroup of ".