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. 

____ f. Every factor group of a torsion-free group is torsion free. 

____ 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