Theorem 3: Finite Subgroup Test Let H be a nonempty finite subset of a group G. If H is closed under the operation of G, then H is a subgroup of G.

Extracted text: Theorem 3: Finite Subgroup Test Let H be a nonempty finite subset of a group G. If H is closed under the operation of G, then H is a subgroup of G.


Extracted text: 2. Provide a two-column proof of Theorem 3: Finite Subgroup Test. 3. Provide a two-column proof: If H and K are subgroups of G, show that H > K is a subgroup of G. 3. Find a noncyclic subgroup of order 4 in U(40).