Question

If o(G)=p where pis a prime number then the group of G is

Answer 1

Answer:

Every p-group is periodic since by definition every element has finite order. If p is prime and G is a group of order pk, then G has a normal subgroup of order pm for every 1 ≤ m ≤ k. This follows by induction, using Cauchy's theorem and the Correspondence Theorem for groups.