Mark each of the following true or false. 

___ a. The nonzero elements of every finite field form a cyclic group under multiplication. 

___ b. The elements of every finite field form a cyclic group under addition. 

___ c. The zeros in C of (x²⁸ - 1) ∈ Q[x] form a cyclic group under multiplication. 

___ d. There exists a finite field of 60 elements. 

___ e. There exists a finite field of 125 elements.

___ f. There exists a finite field of 36 elements. 

___ g. The complex number i is a primitive 4th root of unity. 

___ h. There exists an irreducible polynomial of degree 58 in Z₂[x]. 

___ i. The nonzero elements of Q form a cyclic group Q^* under field multiplication. 

___ j. If F is a finite field, then every isomorphism mapping F onto a subfield of an algebraic closure F̅ of F is an automorphism of F.