Mark each of the following true or false. 

___ a. Every abelian group of prime order is cyclic. 

___ b. Every abelian group of prime power order is cyclic. 

__ c. Z₈ is generated by {4, 6}. 

__ d. Z₈ is generated by { 4, 5, 6}. 

___ e. All finite abelian groups are classified up to isomorphism by Theorem 11.12. 

___ f. Any two finitely generated abelian groups with the same Betti number are isomorphic. 

___ g. Every abelian group of order divisible by 5 contains a cyclic subgroup of order 5. 

___ h. Every abelian group of order divisible by 4 contains a cyclic subgroup of order 4. 

___ i. Every abelian group of order divisible by 6 contains a cyclic subgroup of order 6. 

___ j. Every finite abelian group has a Betti number of 0.