A couple of questions I had hard time solving (and not succeeded).
1. We showed that for every p-sylow group P in G, the following is true:
. Show that equation isn't true for some subgroup H (not sylow) of (symmetric group), meaning .
I don't fully understand how to do this without doing it brute-force, by applying all elements of G on the chosen H.
2. H is a subgroup of , created by the cycle (1234).
(a) Show that for
(b) Show that is a 2-sylow subgroup of G.
I have some difficulty by showing that too.
I will very appreciate any help.