Abstract Algebra (Factor Group Quiz)

1. It makes a sense to speak of the factor group G/N if and only if N is a normal sub-group of the group G.

• True

• False

2. Every sub-group of an abelian group G is a normal sub-group of G.

• True

• False

3. An inner automorphism of an abelian group must just be an identity map.

• True

• False

4. Every factor group of a finite group is again a finite order.

• True

• False

5. Every factor group of a torsion group is a torsion group.

• True

• False

6. Every factor group of a torsion-free group is a torsion free.

• True

• False

7. Every factor group of an abelian group is abelian.

• True

• False

8. Every factor group of a nonabelian group is nonabelian.

• True

• False

9. Z/nZ is a cyclic order of n.

• True

• False

10. R/n is cyclic of order n, where nR ={nr/r E R} and R is under addition.

• True

• False