MATH
hw6.pdf

# hw6.pdf - MODERN ALGEBRA 1 HOMEWORK 6(1 Chapter 2 8.3(2...

• Homework Help
• 1

This preview shows page 1. Sign up to view the full content.

MODERN ALGEBRA 1: HOMEWORK 6 (1) Chapter 2: 8.3 (2) Chapter 2: 8.6 (3) Chapter 2: 12.5 (4) Let H G be a subgroup. The normalizer of H , denoted by N ( H ) , is defined by N ( H ) = { g G | gHg - 1 = H } . (a) Show that N ( H ) is a subgroup of G and N ( H ) = G if and only if H / G . (b) Show that H is a normal subgroup of N ( H ) . Remark. Keep in mind that saying gHg - 1 = H is not the same as saying ghg - 1 = h for every h H . By gHg - 1 = H we mean that the collection { ghg - 1 | h H } as a whole is the same as the collection { h | h H } . (5) Let G = GL 2 ( R ) and H G the subgroup of diagonal matrices, namely matrices of the form a 0 0 b , ab 6 = 0. Find N ( H ) and identify the quotient group N ( H ) / H . (Optional) Generalize the previous result to GL n ( R ) . (6) Let Q =
This is the end of the preview. Sign up to access the rest of the document.
• Fall '17
• jane smith

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern