I had this question on an exam today and I'm not sure how to do it.
"Let G = x . List all the Sylow 2-subgroups of G, and all the Sylow 3-subgroups of G, giving reasons that your lists are complete"
I found that G has order 36, and so I determined that = 1, 3 or 9 and that = 1 or 4 (where denotes the number of Sylow i-subgroups) but from there I couldn't do much. By brute force I managed to find one subgroup of order 4 and one of order 9, so in the end I just put that = 1 and = 1.
Can anyone verify, or correct this?
You're right. Drexel apparently misread and thought you were talking of and not of ...or perhaps
he thought to mention the 3-Sylow sbgps. of as a hint for you.
Anyway, his description gives you some hints: any 3-Sylow sbgp. of G will be the product of with a sbgp. of order 3 of ...