Abstract Algebra question

  • #1

Homework Statement


Let G be a group with pk elements, where p is a prime number and k is greater than or equal to 1. Prove that G has a subgroup of order p.


The Attempt at a Solution


I attempted to prove this by showing that the conditions for a set to be subgroup form a subgroup of order p. I have become lost, however, in my proof. Any direction would be helpful. :-)
 

Answers and Replies

  • #2
22,097
3,283
Hi PhysicsUnderg! :smile:

Take an element g of G. What is the order of g?
 

Related Threads on Abstract Algebra question

  • Last Post
Replies
5
Views
4K
  • Last Post
Replies
4
Views
985
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
0
Views
897
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Top