Subgroup

algebra

Definition

Subgroup

A group is a subgroup of group , denoted as , if the following axioms are fulfilled:

1. Non-Empty Subset:
2. Associativity:
3. Closure (Algebra):
4. Neutral Element:
5. Inverse Element:

Example:

• (not inversible)

Subgroup Criteria

Subgroup Criteria

\end{cases} \ \

&\Longleftrightarrow \begin{cases}

1. & U \neq \emptyset \
2. & \forall x, y \in U: x \circ y^{-1} \in U
   \end{cases}
   \end{align}