Definition Subgroup
Let $G$ be a group. A subset $U \subset G$ is called a subgroup of $G$ if:
1. | $e \in U$ (Neutral element of $G$ is in $U$) |
2. | $a, b \in U \Rightarrow a \circ b \in U$ (Closure) |
3. | $a \in U \Rightarrow a^{-1} \in U$ (Inverses) |
Let $G$ be a group. A subset $U \subset G$ is called a subgroup of $G$ if:
1. | $e \in U$ (Neutral element of $G$ is in $U$) |
2. | $a, b \in U \Rightarrow a \circ b \in U$ (Closure) |
3. | $a \in U \Rightarrow a^{-1} \in U$ (Inverses) |