
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 11th, 2013, 05:01 AM  #1 
Newbie Joined: Oct 2012 Posts: 4 Thanks: 0  Number of subgroups of infinite abelian group
Is the number of subgroups of an infinite abelian group always infinite ? ( or Is there any infinite abelian group having only finite number of subgroups ? ) 
April 12th, 2013, 09:27 AM  #2  
Senior Member Joined: Aug 2012 Posts: 2,323 Thanks: 715  Re: Number of subgroups of infinite abelian group Quote:
If not, then every element of the group has finite order; in which case each element generates a cyclic subgroup of finite size. Since the group is infinite, there must be infinitely many cyclic subgroups.  
May 27th, 2013, 08:26 AM  #3 
Newbie Joined: Oct 2012 Posts: 4 Thanks: 0  Re: Number of subgroups of infinite abelian group
Thank you Maschke !


Tags 
abelian, group, infinite, number, subgroups 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
isomorphic Subgroups of an infinite cyclic Group  Belov  Abstract Algebra  1  April 28th, 2013 01:51 PM 
Subgroups of Abelian Groups  gaussrelatz  Abstract Algebra  9  July 9th, 2012 09:09 AM 
A torsion free abelian group G having a free abelian subgrou  johnmath  Abstract Algebra  9  April 25th, 2011 10:58 AM 
Subgroups of the Group Z^2  sto4432  Abstract Algebra  3  April 30th, 2009 07:17 PM 
Subgroups of the Group Z^2  sto4432  Number Theory  1  December 31st, 1969 04:00 PM 