My Math Forum Normal Subgroups

 Abstract Algebra Abstract Algebra Math Forum

 June 21st, 2017, 03:09 PM #1 Member   Joined: Apr 2017 From: India Posts: 73 Thanks: 0 Normal Subgroups If H is a subgroup such |G:H|=3, then H is a normal subgroup of G. Well, I have read both Lagrange and Sylow theorems but still I am unable to solve this problem. I know if |G:H|=2, then for sure H is a normal subgroup. Please help me out with this question. It seems tricky to me. Last edited by skipjack; June 21st, 2017 at 03:19 PM.
 June 21st, 2017, 03:19 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,935 Thanks: 2209 I think H needn't be a normal subgroup of G. Where did you get this problem from? Was any additional information given?
 June 21st, 2017, 11:35 PM #3 Member   Joined: Apr 2017 From: India Posts: 73 Thanks: 0 Actually, it was like a true / False statement, So it may happen that it is false,Well in that case what is the reason for falsification of the statement?
 June 22nd, 2017, 02:00 AM #4 Member   Joined: May 2017 From: Russia Posts: 34 Thanks: 5 Symmetric group $\displaystyle S_4$ has a subgroup of order 8, which is not normal.
June 22nd, 2017, 02:40 AM   #5
Global Moderator

Joined: Dec 2006

Posts: 20,935
Thanks: 2209

Quote:
 Originally Posted by shashank dwivedi I know if |G:H|=2, then for sure H is a normal subgroup.
That is well-known and is proved here. Scroll down to see a counterexample for the case where |G:H|=3.

There is a related theorem given and proved here that you might find interesting.

 Tags normal, subgroups

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post dpsmith Abstract Algebra 1 January 15th, 2017 03:38 PM BrettsGrad Abstract Algebra 2 February 20th, 2013 08:28 AM Fernando Abstract Algebra 2 July 5th, 2012 11:09 AM donwu777 Abstract Algebra 1 December 10th, 2008 04:03 PM bjh5138 Abstract Algebra 1 October 7th, 2007 09:20 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top