Mark each of the following true or false.
________a. Every factor group of a cyclic group is cyclic.
________b. A factor group of a noncyclic group is again noncyclic.
________c. ℝ/ℤ under addition has no element of order 2.
________d. ℝ/ℤ under addition has elements of order n for all n ϵ ℤ+.
________e. ℝ/ℤ under addition has an infinite number of elements of order 4.
________f. If the commutator subgroup C of a group G is {e}, then G is abelian.
________g. If G/H is abelian, then the commutator subgroup C of G contains H.
________h. The commutator subgroup of a simple group G must be G itself.
________i. The commutator subgroup of a nonabelian simple group G must be G itself.
________j. All nontrivial finite simple groups have prime order.
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