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March 21st, 2009, 09:51 AM   #1
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Symmetric Groups

1. Show that for all .
2. Show that if is prime, where is any transposition and is any p-cycle.
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.
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March 24th, 2009, 09:22 AM   #2
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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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