Quiz3Problems

Quiz3Problems - Quiz 3 Practice Problems Math 332, Spring...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Quiz 3 Practice Problems Math 332, Spring 2010 Questions on Groups 1. Let G = U (15), and let N = { 1 , 4 } . Determine the isomorphism type of G/N . 2. Let G = S 4 , and let N = { e, (1 2)(3 4) , (1 3)(2 4) , (1 4)(2 3) } . Determine the order of the element (1 2 3 4) N in G/N . 3. Let G = D 8 , and let N = { e, s, r 4 , r 4 s } . Is N is a normal subgroup of D 8 ? Explain. 4. Let G be an abelian group, and let N be a normal subgroup of G . Prove that G/N is abelian. 5. Let ϕ : Z 3 × Z 3 Z 3 be a homomorphism, and suppose that ϕ (1 , 0) = 1 and ϕ (0 , 1) = 2. List the elements in the kernel of ϕ . 6. Let G and H be groups, and define a function π : G × H G by π ( g,h ) = g. Prove that π is a homomorphism. 7. Let G be a group, let ϕ : G G be a homomorphism, and let S = { g G | ϕ ( g ) = g } . Prove that S G . 8. List all isomorphism types of abelian groups of order 900. 9.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

Quiz3Problems - Quiz 3 Practice Problems Math 332, Spring...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online