Quiz2Solutions

# Quiz2Solutions - Math 332 Spring 2010 Quiz Name 1[8 points...

This preview shows pages 1–5. Sign up to view the full content.

Math 332, Spring 2010 Name: __________________________________ Quiz # 1. Let be the group of integers under addition, and let be the group [8 points] Z Z K À + − " + ! " œ under the operation of matrix multiplication. Prove that is isomorphic to . K Z

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

View Full Document
2. Consider the following subgroup of : [8 points] ^ ‚ ^ ' \$ L œ e f a b a b a b a b a b a b . Determine the cosets of in . (That is, list the elements in each of the three cosets.) L ^ ‚ ^ ' \$ 3. Let Aut , and suppose that and . Express as a permutation c d 8 points ! ! ! ! H < œ < = œ <= a b a b a b # of the elements of the set . e f /ß <ß < ß < ß < ß =ß <=ß < =ß < =ß < = # \$ % # \$ %
4. [6 points (3 pts each)] (a) Determine the isomorphism type of . Express your answer as a direct product of cyclic a b groups. (b) Compute mod . # 5. Find an element of order in . [6 points] W ‚ ^ "!

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Quiz2Solutions - Math 332 Spring 2010 Quiz Name 1[8 points...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online