Mark each of the following true or false. 

___ a. Any two Sylow p-subgroups of a finite group are conjugate. 

___ b. Theorem 36.11 shows that a group of order 15 has only one Sylow 5-subgroup. 

___ c. Every Sylow p-subgroup of a finite group has order a power of p. 

___ d. Every p-subgroup of every finite group is a Sylow p-subgroup. 

___ e. Every finite abelian group has exactly one Sylow p-subgroup for each prime p dividing the order of G. 

___ f. The normalizer in G of a subgroup H of G is always a normal subgroup of G. 

___ g. If His a subgroup of G, then His always a normal subgroup of N[H]. 

___ h. A Sylow p-subgroup of a finite group G is normal in G if and only if it is the only Sylow p-subgroup of G. 

___ i. If G is an abelian group and H is a subgroup of G, then N[H] = H. 

___ j. A group of prime-power order pⁿ has no Sylow p-subgroup.