March 21st, 2009, 10:51 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, 10:22 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.


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