Its mentioned that |G|=p^2q where p and q are two distinct prime numbers. By applying slyow’s 3rd theorem,
we can see that
number of p-sylow subgroups= 1+2p ….………………..(1)
number of q-sylow subgroups= 1+q ……………………….(2)
- clearly from (1) option A will always be correct
- its not always possible to have normal p-sylow subgroup as nothing about the elements is mentioned.
- from (2) is can be seen that option 3 is false
- again from (2) option D is false.