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 isomoiphic.
— 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.
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