Mark each of the following true or false.___ a. It makes sense to speak of the factor grou...

Mark each of the following true or false.

___ a. It makes sense to speak of the factor group G/N if and only if N is a normal subgroup of the group G.

__b. Every subgroup of an abelian group G is a normal subgroup of G.

__ c. An inner automorphism of an abelian group must be just the identity map.

__ d. Every factor group of a finite group is again of finite order.

__e. Every factor group of a torsion group is a torsion group. (See Exercise 22.)

__f. Every factor group of a torsion-free group is torsion free. (See Exercise 22.)

__ g. Every factor group of an abelian group is abelian.

__ h. Every factor group of a nonabelian group is nonabelian.

__i. ℤ/nℤ is cyclic of order n.

__j. ℝ/nℝ is cyclic of order n, where nℝ= {nr| r € ℝ} and ℝ is under addition.