solution7 - PMath 336: Introduction to Group Theory...

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

View Full Document Right Arrow Icon
PMath 336: Introduction to Group Theory Exercise set 7 July 11, 2008 Solution should be submitted by the end of the Monday lecture of the following week, either in class or in the submission box. You may not submit joint or identical works. Notation GL n ( S ) : Invertible n × n matrices with coefficients in S , under multiplication D n : The group of symmetries of the regular n -gon S n : The group of permutations of 1 ,...,n Z : The group of integers under addition Z n : The group { 0 ,...,n - 1 } with addition modulo n U n : The group of numbers less than n and prime to n , with multiplication mod n . Q (quaternions): The subgroup of GL 2 ( C ) generated by i = ± 0 i i 0 ² and j = ± 0 1 - 1 0 ² . Questions 1. [12] Write each of the following permutations as a product of disjoint cycles, and as a product of transposi- tions, and compute its order. (a) ± 1 2 3 4 2 4 3 1 ² (b) ± 1 2 3 4 5 6 7 8 9 4 2 5 7 3 6 1 9 8 ² (c) ± 1 2 3 4 5 2 4 5 1 3 ² Solution: (a) (124) = (12)(24). The order is 3. (b) (147)(35)(89) = (14)(47)(35)(89). The order is 6.
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.

This note was uploaded on 04/27/2010 for the course PMATH 336 taught by Professor Moshekamensky during the Spring '08 term at Waterloo.

Page1 / 2

solution7 - PMath 336: Introduction to Group Theory...

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