Mark each of the following true or false. 

___ a. Every group of order 159 is cyclic. 

___ b. Every group of order 102 has a nontrivial proper normal subgroup. 

___ c. Every solvable group is of prime-power order. 

___ d. Every group of prime-power order is solvable. 

___ e. It would become quite tedious to show that no group of nonprime order between 60 and 168 is simple by the methods illustrated in the text. 

___ f. No group of order 21 is simple. 

___ g. Every group of 125 elements has at least 5 elements that commute with every element in the group. 

___ h. Every group of order 42 has a normal subgroup of order 7. 

___ i. Every group of order 42 has a normal subgroup of order 8. 

___ j. The only simple groups are the groups Z_P and A_n where p is a prime and n ≠ 4.