Conditions for a subset to be a subgroup

Dependencies:

  1. Group
  2. Subgroup
  3. Identity of a group is unique
  4. Inverse of a group element is unique

Let $H$ be a subset of $G$. $H$ is a subgroup of $G$ iff

Proof

Dependency for:

  1. Condition for a subset to be a subgroup
  2. Cyclic Group

Info:

Transitive dependencies:

  1. Group
  2. Identity of a group is unique
  3. Subgroup
  4. Inverse of a group element is unique