Hi there,
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?
Many thanks