Re: Aut A5 = S5

From: Robin Chapman (rjc_at_ivorynospamtower.freeserve.co.uk)
Date: 10/27/04 

Date: Wed, 27 Oct 2004 12:01:59 +0100

Kira Yamato wrote:

> Robin Chapman wrote:
>> Kira Yamato wrote:
>>
>>
>>>I've been banging my head on this problem from algebra for days.
>>>
>>>Show that the automorphism group of the alternating group of 5 elements
>>>is isomorphic to the symmetric group of 5 elements.
>>
>>
>> You could show that A_5 has 5 subgroups of order 12.
>>
>
> Um... Could you please elaborate a bit more? I'm really getting stuck
> on this one. Thanks.

Well, aut(A_5) will act on the set of order 12 subgroups of A_5. 

-- 
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_

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