Prove Subgroup Exists in Abelian Group of Order m, n Divides m

  • Thread starter Thread starter Hams
  • Start date Start date
  • Tags Tags
    Algebra
Join the discussion
Registration is free. Start your own thread to ask a follow-up.
Sign up Log in
1 reply · 2K views
Hams
Messages
2
Reaction score
0
1. Let G be an abelian group of order m. If n divides m, prove that G has a subgroup of order n .
 
Physics news on Phys.org

Discussion

please could anyone help to find out the solution of this question or give me some hints.
Thanks.
 

Similar threads

Proving that an Abelian group of order pq is isomorphic to Z_pq
  • Mr Davis 97
  • · Replies 5 ·
  • Calculus and Beyond Homework Help
Replies
5
Proving a group of order mn is cyclic given elements of order m and n
  • cragar
  • · Replies 3 ·
  • Calculus and Beyond Homework Help
Replies
3
Prove that a group of order (m^2)(n^2) is abelian if it has all normal subgroups
  • Sprooth
  • · Replies 14 ·
  • Calculus and Beyond Homework Help
Replies
14
Show abelian group has element of order [m,n]
  • TopCat
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
Proving Finite Order Elements Form a Subgroup of an Abelian Group
  • rideabike
  • · Replies 2 ·
  • Calculus and Beyond Homework Help
Replies
2
Solutions to x^m = e in a cyclic group of order n
  • jmjlt88
  • · Replies 6 ·
  • Calculus and Beyond Homework Help
Replies
6
Why does an abelian group of order G have G conjugacy classes
  • Dixanadu
  • · Replies 1 ·
  • Calculus and Beyond Homework Help
Replies
1
Graduate For every positive integer n there is a unique cyclic group of order n
  • BomboshMan
  • · Replies 6 ·
  • Linear and Abstract Algebra
Replies
6
Proving an Abelian Group with 2 Elements of Order 2 has a Subgroup of Order 4
  • 188818881888
  • · Replies 9 ·
  • Calculus and Beyond Homework Help
Replies
9
Proving a cyclic group of order n has exactly one subgroup of order r
  • murmillo
  • · Replies 1 ·
  • Calculus and Beyond Homework Help
Replies
1