Abstract Algebra: L15, first isomorphism theorem and select applications, 10-5-16

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You begin by talking about two groups G nd G' then introduce the concept of a homomorphism "phi" from G to G'. That's fine, but you never state 'let G be G/ker phi which would have made things clearer to the kids. Then you write the range as { e, phi(b), phi(ab), } which should be written in terms of phi, that is phi(e)=e.. But what's really confusing is that you talk about the squaring function not being one-one. Why? This may be the reason the kids appear to you to be confused and you say"I think I made a mistake or something like that. You are about to prove a difficult theorem and you appear unprepared.

josephtursi