Let Q be the group of quaternions. Show that Aut(Q) is isomorphic to S4.
Any help here would be really appreciated!
(Also, sorry, I'm new, so I'm not really sure about how posting on here works.)
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http://math.stackexchange.com/questions/195932/automorphism-group-of-the-quaternion-group – Prahlad Vaidyanathan Sep 27 '13 at 10:59
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Presumably $S_4$ is the symmetric group on four elements? You might want to explain $\operatorname{Aut}(Q)$, because I can think of a few things it could mean. (Perhaps there is an "obvious" interpretation to people more familiar with quaternions, and I think I can guess from the fact it should be isomorphic to $S_4$, but it would be nice to clarify). You should also say what you have already tried, or be more specific about what you don't understand. – mdp Sep 27 '13 at 11:01
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@user95169 sorry for badly treating your edit maybe you can edit again i will accept it... – user577215664 Oct 25 '23 at 11:16
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Hint: $S_4$ is the permutation group of four elements, can you think of how you can use a permutation to define an isomorphism ? What four elements of $Q$ will you permute ?
Belgi
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You might want to have a look at this paper/hint, where also a nice geometrical interpretation is given.
Nicky Hekster
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