# Abstract Algebra/Group Theory/Subgroup/Definition of a Subgroup

< Abstract Algebra | Group Theory | Subgroup

Let G be a group with binary operation

- Subgroup H of Group G

- is a group
- is a subset of G
- shares with G

< Abstract Algebra | Group Theory | Subgroup

Let G be a group with binary operation $\ast$

- Subgroup H of Group G

- is a group
- is a subset of G
- shares $\ast$ with G