1 / 4

Test Corrections

Test Corrections. You may correct the in-class portion of your test . You will get back 1/2 of the points you lost if you submit correct answers. This work is to be done on your own (or in consultation with me only). Skidmore Honor Code!

quade
Download Presentation

Test Corrections

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Test Corrections • You may correct the in-class portion of your test. You will get back 1/2 of the points you lost if you submit correct answers. • This work is to be done on your own (or in consultation with me only). Skidmore Honor Code! • Corrections should be done on separate sheets, NOT on the original test. Hand both things in, NOT stapled together. • Due on Tuesday (11/26) at 4:45.

  2. More on Homomorphisms (11/22) • “First Isomorphism Theorem”. If  is an homomorphism from G to G’, then the image of , (G) is isomorphic to G / Ker  . • Proof. We’ve pretty much already done it. Define  from G/ Ker  to (G) by (a Ker) = (a). We showed last time that  is well-defined, one-to-one, and onto. Hence we need only establish OP. But by the definition of coset multiplication, we have ((a Ker )(bKer )) = (a bKer ) = (a b) = (a)(b) = (aKer ) (b Ker )) .

  3. Some Questions • If  is the “natural” modular homomorphism from Z to Zn , What factor group of Z is Zn isomorphic to? • What “well-known” group is GL(2, R) / SL(2, R) isomorphic to? Why? • Terminology: If  is an homomorphism from G to G’, then (G) is called a homomorphic image of G. • If G is abelian, is (G) necessarily abelian? • If (G) is abelian, is G necessarily abelian? • If G is cyclic, is (G) necessarily cyclic? • If (G) is cyclic, is G necessarily cyclic?

  4. Assignment for Monday • Work on test corrections. • On page 220-221 do Exercises 20-27.

More Related