Thread: ı need urgent help

1. Let p be prime, and G be a finite group. If every element of G has order a power of p, then |G| = p^n for some n≥0. (Hint: Use Cauchy’s theorem.)


2. Tell as much as possible about the subgroups of a group of order 30 and of a group of order 40.


( please help me... its emergency for me )

Originally Posted by bogazichili

1. Let p be prime, and G be a finite group. If every element of G has order a power of p, then |G| = p^n for some n≥0. (Hint: Use Cauchy’s theorem.)

Assume that there is such that divides order of . Then by Cauchy's theorem there exists and element of order which is not a power of - a contradiction. Thus, all prime divisors of must be equal to and so .

2. Tell as much as possible about the subgroups of a group of order 30 and of a group of order 40.

I am not sure exactly what you are looking for.
But for order it can be shown (I looked up a classification table) that these groups are: .