- #1

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## Homework Statement

Let p: G-->M be a group homomorphism with ker(p) = K. If a is an element of G, how that Ka = {g in G | p(g) = p(a)}

## Homework Equations

none needed

## The Attempt at a Solution

Okay, I've been struggling with this problem for awhile and I've ran into a problem:

-Let g be an element of Ka

-Let b be an element of K such that ba = g.

Since g is an element of Ka and the intersection of Ka and K is {1}, p(g) does not equal zero.

But then if ba = g then:

p(ba) = p(g)

p(b)p(a) = p(g)

0p(a) = 0, but p(g) can't be zero!

Someone want to shed some light perhaps? I guess I need help on understanding this road block I've run into as well as the actual problem >.<. Thanks!