hw3 - formulas for R i R j R i F j F i R j and F i F j For...

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

Math 113 Homework # 3, due 9/23/9 at 2:10 PM 1. Fraleigh section 4, exercise 41. 2. Fraleigh section 5, exercise 13. 3. (a) Fraleigh section 5, exercise 54. (b) Is this still true if one replaces intersection by union? Prove or give a counterexample. 4. Let n > 1 be an integer and let θ = 2 π/n . Let P be the regular n -gon with vertices (cos iθ, sin ) for i Z n . The dihedral group D n is the symmetry group of P , which consists of rotations R i and reflections F i for i Z n . Here R i is the counterclockwise rotation around the origin by angle , and F i is the reflection across the line through the origin and (cos iθ/ 2 , sin iθ/ 2). Your problem: find (and give at least some justification for) general
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: formulas for R i R j , R i F j , F i R j , and F i F j . For example, R i R j = R i + j , where the addition of indices is mod n . 5. Find all subgroups of D 4 . 6. If G is a group, the center of G is deﬁned to be Z ( G ) = { x ∈ G | xy = yx for all y ∈ G } . (a) Show that Z ( G ) is a subgroup of G . (b) For n > 2, what is the center of D n ? (Use the multiplication rules you found above. The answer depends on whether n is even or odd.) 7. Fraleigh section 6, exercise 32 (justify as always). 8. How challenging did you ﬁnd this assignment? How long did it take?...
View Full Document

{[ 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
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}