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
November 6th, 2010, 10:25 AM   #1
Newbie
 
Joined: Nov 2010

Posts: 7
Thanks: 0

Subgroups

Original Question: Let G be an abelian group of order 540. What is the largest possible number of subgroups of order 3 such a group G can have?

My attempt: The fundamental theorem of group theory says that any group G of order 540 can be expressed as

G1 X G2

where G1 is a group of order 27 and G2 is a group of order 20.

If I'm searching for every group of order 3, then I guess I'm actually searching for every element of order 3. (number of subgroups of order 3= number of elements of order 3 divides by 2). Since an element of order 3 can only be in G1, I need to be searching for elements of order 3 in a group of order 27. This will require classifying all groups of order 27, but I don't know how to classify these groups. Help?
DanielThrice is offline  
 
November 25th, 2010, 03:28 PM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 20,277
Thanks: 1963

Quote:
Originally Posted by DanielThrice
I'm actually searching for every element of order 3.
No, you're trying to find the maximum number of elements of order three in "such a group". It's possible that each non-identity element of G1 has order 3, so that maximum is 26, and so the maximum number of subgroups of order 3 is 13.
skipjack is online now  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
subgroups



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Subgroups gaussrelatz Algebra 1 October 11th, 2012 12:30 AM
Normal subgroups Fernando Abstract Algebra 1 April 11th, 2012 01:40 AM
Number of subgroups of Sn honzik Abstract Algebra 0 February 13th, 2011 07:45 AM
Normal Subgroups ejote Abstract Algebra 4 February 1st, 2011 08:30 AM
no subgroups bjh5138 Abstract Algebra 2 August 14th, 2008 01:03 PM





Copyright © 2019 My Math Forum. All rights reserved.