Subgroup

Definition

A subgroup of a group $(G,{\cdot }_G)$ is a group $(H,{\cdot }_H)$ such that:

• $H\subset G$
• ${\cdot }_H$ is made from restricting ${\cdot }_G$ to $H$, and $\forall h_1,h_2:H.h_1\cdot h_2\in H$
• $H$ is a goup in its own right.

See also

• Normal Subgroup