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February 15th, 2009, 04:44 PM   #1
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Find a abelian subgroup of S5 of order 6

Hi everyone!

I'm trying to solve the above problem and have hit a wall! So far I know the identity is in the subgroup, two elements that commute and their inverses.

I have the subgroup as:
{(5),(4,5),(1,2,3),(1,3,2)

What would the other two elements be? I've had someone tell me that if I multiply some of these elements together I'll get the other two, but every attempt I make, I always end up with elements I already have!!!

If someone could show me what I need to do and if possible the solution to the above problem I'd appreciate it!

Thanks~
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February 16th, 2009, 07:05 AM   #2
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Re: Find a abelian subgroup of S5 of order 6

Do you understand how permutations multiply? For example,(1,2,3)(4,5) is trivially a permutation distinct from the ones you list as it does a different thing to the set {1,2,3,4,5} from any of the others.
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