My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

LinkBack Thread Tools Display Modes
September 25th, 2007, 09:53 AM   #1
Joined: Sep 2007

Posts: 9
Thanks: 0

question on groups

i think i have spent to much time looking at this problem, and i just cant figure it out. i am probably just overlooking something obvious. So here it is.

Let b be an element in some group G, and suppose that b has finite order m. Let c=b^k for some k. Prove that the order of c divides m.
stf123 is offline  
September 25th, 2007, 10:44 AM   #2
Site Founder
julien's Avatar
Joined: Nov 2006
From: France

Posts: 824
Thanks: 7

Well, you have that c^m=b^(km)=(b^m)^k=1 (the unit element). This means that the cyclic subgroup <c> generated by c has an order which is a divisor of m.
julien is offline  

  My Math Forum > College Math Forum > Abstract Algebra

groups, question

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Question on groups Leo_J Abstract Algebra 13 September 12th, 2013 11:34 PM
A question groups and subgroups... Artus Abstract Algebra 2 January 21st, 2013 07:27 AM
Another Question about Quotient Groups yetixhunting Abstract Algebra 5 April 9th, 2011 03:26 PM
question in groups themanandthe Abstract Algebra 6 August 22nd, 2010 10:59 PM
Question regard the T-groups help:-( sastra81 Abstract Algebra 0 January 20th, 2007 02:34 AM

Copyright © 2019 My Math Forum. All rights reserved.