Question

Prove that any subgroup of order p^(n – 1) in a group G of order p^(n)

(p is a prime

number) is normal in G.​

Answer 1

Answer:

Let G be a finite group of order pn, where p is a prime number and n is a positive ... Then prove that H is a normal subgroup of G. ... only one factor of p, we must have either |ker(ϕ)|=pn or |ker(ϕ)|=pn−1.