
Abstract Algebra Abstract Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 31st, 2013, 11:19 AM  #1 
Newbie Joined: Mar 2013 Posts: 2 Thanks: 0  How to disprove these statements?
*Every endomorphism is an epimorphism. *Every two abelian groups of the same order are isomorphic. *Every monomorphism is an isomorphism. I know these statements are false, but I cannot find any example to disprove them. If you know, could you give me some example for these statements? Thanks. 
March 31st, 2013, 11:25 AM  #2  
Newbie Joined: Mar 2013 Posts: 2 Thanks: 0  Re: How to disprove these statements? Quote:
 
March 31st, 2013, 06:43 PM  #3  
Senior Member Joined: Aug 2012 Posts: 1,999 Thanks: 571  Re: How to disprove these statements? Quote:
For #2, think six.  
April 1st, 2013, 02:18 AM  #4 
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5  Re: How to disprove these statements?
Maybe one can give a few more hints: 1) Between any two abelian groups there is always a Homomorphism called the zero Homomorphism. Can you guess what is does? 2) There is only one abelian group of order 6 or of any order that is a square free number (i.e.: is not divisible by the square of a prime). The smallest number n, with more that one abelian group of order n is 4. ( To prove it: guess what the groups are and look at the order of each element in both groups.) 3) A monomorphism does not need to be an endomorphism. So you might want to look a a morphism from a 'small' group into a 'big' group. (small and big are not supposed to refer to any group theoretic terms, they are just to imagen, how an example should look like.) I hope that helps. Tell me if it worked for you. 

Tags 
disprove, statements 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
prove or disprove isomorphism statements  rayman  Abstract Algebra  2  August 18th, 2012 04:30 AM 
Limit statements  layd33foxx  Calculus  8  September 26th, 2011 01:14 PM 
Set Statements  jstarks4444  Applied Math  2  March 10th, 2011 02:00 PM 
What do these statements mean?  rsoy  Physics  1  December 26th, 2010 09:50 PM 
Set Statements  jstarks4444  Number Theory  2  December 31st, 1969 04:00 PM 