Talk:Automorphisms of the symmetric and alternating groups

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Typesetting suggestion

Generic case:

• $n\neq 2,6$: ${\mbox{Aut}}(S_{n})=S_{n}$, and thus ${\mbox{Out}}(S_{n})=1$.

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Generic case:

• $n\neq 2,6:\quad {\mbox{Aut}}(S_{n})=S_{n}{\text{ and thus }}{\mbox{Out}}(S_{n})=1.$

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Which of the two typesetting styles above looks better?

(This hints at some style improvements, I hope.) Michael Hardy 02:04, 21 October 2007 (UTC)

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I see my rhetorical question above was ignored, and that's why the article looks so ugly. Maybe I'll come back in 25 years............. Michael Hardy (talk) 20:16, 29 March 2009 (UTC)

The extensions of A6 by C2

Out(A6) is C2×C2. So there are four order-720 groups which are extensions of A6 by C2. I am aware of

• The direct product A6 × C2
• S6
• M10
• and there must be another one, I don't know if it's isomorphic to M10.

I think it would be helpful to list them, giving a link to M10. Maproom (talk) 17:41, 12 May 2011 (UTC)

Aut(A6) ≅ PΓL(2,9) has three order-720 subgroups: S6, M10, and PGL(2,9). These are listed somewhere on enwiki, but I didn't see them when I looked just now. There is also the direct product A6×C2, and this is the only other extension of a normal subgroup A6 by a quotient C2. SL(2,9) is an extension of the normal subgroup C2 by the quotient group A6. JackSchmidt (talk) 02:32, 13 May 2011 (UTC)

Is C₂ defined here?

I see S₂ = C₂ = Z/2 at 4.1, but shoudn't itC₂ be defined (or at least wikilinked) earlier? (If I knew enough myself I would be bold and do it.) Mark Hurd (talk) 08:08, 7 August 2012 (UTC)

Shouldn't what be defined? Incidentally, I suspect that Z/2 is a typo for Z/2Z, and there's a similarly wrong Z/3 in the next paragraph. Maproom (talk) 11:22, 7 August 2012 (UTC)

C₂, as I intimated in the heading. Mark Hurd (talk) 16:33, 7 August 2012 (UTC)

Sorry, yes. I often forget to read headings.

Would it help if, the first time "C₂" appears in the article, it were wikilinked to Cyclic group? Are there people reading this article who don't know what "C₂" refers to, but do understand "Aut(..)" and "Out(..)"? Or should these also be wikilinked when they first appear in this article? Maproom (talk) 21:57, 7 August 2012 (UTC)

Well, I'm reading this and I have an Honours degree in Mathematical Sciences (B.Sc.(Ma.)(Hons.)), but that included a lot of computer science (as much as possible, actually), so I'd get more of this if the "little" details were wikilinked on "first use". Where "first use" can skip use with in <math> tags, as long as it is explained soon after. Mark Hurd (talk) 02:16, 8 August 2012 (UTC)

NB I can guess Aut and Out because of the wikilinks in the first line of the article. Mark Hurd (talk) 02:22, 8 August 2012 (UTC)

Title

This article is really about Out(S_6), isn't it? I like "The exceptional outer automorphism of S6", but that's already a redirect here, ISTR that messes up the move command. --GodMadeTheIntegers (talk) 16:31, 27 April 2015 (UTC)

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suggestion

Who in their right mind would denote the trivial group by $C_1$?? — Preceding unsigned comment added by 2A01:CB00:688:9A00:4546:8E27:D5B3:C4C0 (talk) 14:04, 9 May 2020 (UTC)

Effect of the outer automorphism on cycle structure

The section "Construction from Graph Partitions" says that "cycle lengths are preserved," which I believe is simply wrong. It is contradicted in the section "Structure of Outer Automorphism" which I believe is correct. If the earlier section is trying to say something different from the apparent meaning (that elements such as (12) are mapped to other two-cycles), please clarify ... otherwise, please correct. J-weinstein77 (talk) 03:49, 19 May 2020 (UTC)

Too technical?

2602:304:B1AE:E770:26FD:52FF:FE74:FAAC (talk) 17:15, 13 May 2021 (UTC)