The Road to Reality http://www.roadtoreality.info/ 

Exercise [13.04] http://www.roadtoreality.info/viewtopic.php?f=19&t=176 
Page 1 of 1 
Author:  Sameed Zahoor [ 12 Jul 2008, 10:38 ] 
Post subject:  Exercise [13.04] 
We are given, 1. 2. 3. a) We have, (using 3) b) Consider the identity Now, (using 3) or or(using 3 again) or c) We have, (using 3) (using 3) d) It is merely a restatement of 2.() 
Author:  deant [ 18 Jul 2010, 16:11 ] 
Post subject:  Re: Exercise [13.04] 
Given only 1, 2, and 3, there is no mention of any "1" element. There are only 1, i, C, and various multiplications of these. Now rule (1) allows you to cancel any 4 i's multiplied in a row; Rule (2) allows you to cancel any 2 C's multiplied in a row; and rule (3) allows you to take any 'string' of i's and C's, and move all the C's to the right, e.g. CiiCi = CiiiiiC (3) = CiC (1) = iiiCC (3) = iii (2) So, each element of the group can be represented as (03 i's)(0 or 1 C). The 8 distinct elements are thus: 1, i, ii, iii, C, iC, iiC, and iiiC. ..of course there's no reason you can't then denote i^2 as '1', but it makes no difference to the structure of the group. 
Page 1 of 1  Archived: 07 Aug 2014 
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group http://www.phpbb.com/ 