March 21st, 2009, 09:51 AM  #1 
Newbie Joined: Mar 2009 Posts: 21 Thanks: 0  Symmetric Groups
1. Show that for all . 2. Show that if is prime, where is any transposition and is any pcycle. 3. Show that is a proper subgroup of . What is the isomorphism type of this subgroup? It seems like if I could do 1, then 2 and 3 would follow pretty easily...I'm not sure. 
March 24th, 2009, 09:22 AM  #2 
Senior Member Joined: Dec 2008 Posts: 160 Thanks: 0  Re: Symmetric Groups
The only thing you need to show for 1 and 2 is that in ech case there is sequence of operations that exchange any two elements, while keeping the rest.


Tags 
groups, symmetric 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
About minimal normal groups and subnormal groups  Sheila496  Abstract Algebra  0  October 20th, 2011 09:45 AM 
Symmetric group S4  andmar  Abstract Algebra  3  October 8th, 2011 10:48 AM 
For a curve to be symmetric?  jaredbeach  Algebra  2  August 19th, 2011 04:41 AM 
Homomorphism of Lie groups as groups but not as manifolds  lime  Abstract Algebra  3  October 25th, 2010 07:30 AM 
If A and B are symmetric, show A+B is also symmetric  happygolucky88  Linear Algebra  1  September 3rd, 2009 06:51 AM 