- #1

Halaaku

- 23

- 0

## Homework Statement

define a function f--> gHg[itex]^{-1}[/itex]

## Homework Equations

prove if f is 1-1 and onto.

## The Attempt at a Solution

1-1:

f(h1)=f(h2)

gh1g[itex]^{-1}[/itex]=gh2g[itex]^{-1}[/itex]

h1=h2 (left and right cancellations)

onto:

f(g[itex]^{-1}[/itex]hg)=gg[itex]^{-1}[/itex]hgg[itex]^{-1}[/itex]=h

so every h belonging to H has an image of g[itex]^{-1}[/itex]hg.

However,I do not really understand the last line. I followed the example that we did in class but now I am not sure.