GRE Subject 2026 Practice Test Maths Abstract Algebra Free Quiz 1

1. What type of group has a commutative operation?

A. Cyclic B. Finite C. Infinite D. Abelian

2. What is a ring?

A. Group B. Ring C. Field D. Module

3. What is a field?

A. Field B. Ring C. Group D. Vector space

4. Do the integers Z form a ring?

A. Group only B. Field C. Ring D. Vector space

5. What is a subgroup?

A. Ring B. Subgroup C. Field D. Module

6. What is a quotient group?

A. Subgroup B. Product C. Quotient group D. Direct sum

7. What is a structure-preserving map between algebraic structures?

A. Isomorphism B. Automorphism C. Endomorphism D. Homomorphism

8. What is an isomorphism?

A. Homomorphism B. Isomorphism C. Automorphism D. Epimorphism

9. What is the symmetric group S_n?

A. Cyclic B. Abelian C. Symmetric D. Infinite

10. What is the alternating group A_n?

A. Odd permutations B. Abelian C. Cyclic D. Even permutations