x Turn on thread page Beta
 You are Here: Home >< Maths

# Proof of a proposition about homomorphisms watch

1. I was reading a proof about a proposition, but I'm not sure what the phrase " restricts to an isomorphism from to " really means. I was trying to figure it out from the diagram, but I was a bit confused...

Attached Images

2. (Original post by Artus)
I was reading a proof about a proposition, but I'm not sure what the phrase " restricts to an isomorphism from to " really means. I was trying to figure it out from the diagram, but I was a bit confused...

In general, if we have a homomorphism , and we have , to say that phi restricts to an isomorphism from C to D means that (i.e. the image of C under phi is D), and that the restriction is an isomorphism.
3. To add to the above - in this instance, it just means apply the isomorphism to elements of the form: . The condition says that the isomorphism on the semidirect product takes such elements to elements of the form bijectively

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 18, 2013
Today on TSR

### Loughborough better than Cambridge

Loughborough at number one

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams