Group/Subgroup/Definition

Subgroup

Let ${}(G,e,\circ )$ be a group. A subset ${}H\subseteq G$ is called a subgroup of ${}G$, when the following conditions hold.

1. ${}e\in H$.
2. If ${}g,h\in H$, then also ${}g\circ h\in H$.
3. If ${}g\in H$, then also ${}g^{-1}\in H$.