My Math Forum  

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

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 1st, 2011, 01:30 PM   #1
Newbie
 
Joined: May 2011

Posts: 9
Thanks: 0

Nice order problem on subgroups

Let G be a finite group with a normal subgroup N such that |N| and [G: N] are relatively prime. Prove that N is the only subgroup of G whose order is order |N|.
Hint:
Assume H is a subgroup of G with |H|=|N|, and let a homomorphism go from G to G/N. What does this homomorphism say of the order of the image of H,or H itself?
matheart is offline  
 
May 1st, 2011, 01:56 PM   #2
Senior Member
 
Joined: Jun 2010

Posts: 618
Thanks: 0

Re: Nice order problem on subgroups

matheart,

What have you tried so far? Did the hints not help?

-Ormkärr-
 is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
nice, order, problem, subgroups



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Again, nice problem! tva_vlad Number Theory 12 September 25th, 2013 08:04 PM
nice problem UltraMath Algebra 15 September 11th, 2011 08:19 PM
Subgroups Containing All Elements of Order n Cider Abstract Algebra 1 February 24th, 2010 07:18 AM
Nice Sphere Problem yaDDy Algebra 0 July 24th, 2008 12:34 PM
Nice problem,Algebra. Endless Calculus 2 December 8th, 2007 12:37 PM





Copyright © 2019 My Math Forum. All rights reserved.