📂Abstract Algebra

Definition and Test Method of Subgroups

Definition¹

group $G$의 subset $H$가 $G$의 연산에 대해서 group일 때, $H$를 $G$의 subgroup이라 하고 다음과 같이 표기한다.

$$ H \le G $$

Explanation

If $H$ is a subgroup of $G$ that is not equal to $G$, it is called a proper subgroup, and is denoted as follows.

$$ H \lt G, \qquad H \lneq G $$

For any group $G$ with identity $e \in G$, $\left\{ e \right\}$ is always a subgroup of $G$; this is called the trivial subgroup. A subgroup that is not trivial is called a nontrivial subgroup.

See also

• Subgroup criterion