S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Mon, 22 Dec 2014 19:23:54 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 2 posts ] 
Author Message
PostPosted: Sun, 2 Nov 2003 00:28:13 UTC 
Offline
Senior Member

Joined: Sun, 28 Sep 2003 21:18:37 UTC
Posts: 69
1. U = {z is an element of C such that the absolute value of z = 1)

Show that U is a subgroup of (C, *).

2. Un = {z is an element of C such that z^n = 1}

Show that for each positive integer n >= 2, Un is a subgroup of (C, *). To what groups is Un isomorphic?


Top
 Profile  
 
PostPosted: Sun, 2 Nov 2003 08:43:42 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9861
Mathman wrote:
1. U = {z is an element of C such that the absolute value of z = 1)

Show that U is a subgroup of (C, *).


To prove that a group H is a subgroup of another group G under multiplication, you need to show the following:

1) H is closed under muliplication
2) The identity element e of G is contained in H
3) If a\in G is an element of H, then so is a^{-1}

Mathman wrote:
...To what groups is Un isomorphic?


My suggestion would be to multiply arbitrary elements of U_n together and see what you get. Start with small examples, such as U_4.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA