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. 
Re: How to disprove these statements? Quote:

Re: How to disprove these statements? Quote:
For #2, think six. 
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. 
All times are GMT 8. The time now is 04:41 PM. 
Copyright © 2019 My Math Forum. All rights reserved.