A1.4 B1.3

Groups, Rings and Fields
Part II, 2001

(i) Define the notion of a Sylow pp-subgroup of a finite group GG, and state a theorem concerning the number of them and the relation between them.

(ii) Show that any group of order 30 has a non-trivial normal subgroup. Is it true that every group of order 30 is commutative?