What are the usual tricks is proving that a group is not simple? (Perhaps a link to a list?)
Also, I may well be being stupid, but why if the number of Sylow p groups $n_p=1$ then we have a normal subgroup?
What are the usual tricks is proving that a group is not simple? (Perhaps a link to a list?)
Also, I may well be being stupid, but why if the number of Sylow p groups $n_p=1$ then we have a normal subgroup?