Re: Complete Groups / S_6

Article View: sci.math.research

Article #110

#110

From: John C. Baez
Date: Mon, 28 Sep 1992 23:30

12 lines
1381 bytes

In article <1992Sep28.201204.13907@tamsun.tamu.edu> rlm7638@tamsun.tamu.edu (Jack McKinney) writes:
>     A complete group is one that is isomorphic to its group of
>Automorphisms. The symmetric group on n elements is complete for
>all integers n _except_ 2 and 6. It is also true that the outer
>automorphisms of S_6 form one coset to the set of inner automorphisms.
>Can someone provide an outer automorphism on S_6 ? (This would
>completely specify Aut(S_6), which is isomorphic to S_6 x Z_2)

There was a thread on sci.math where we talked about this.  There is
a nice construction due to Sylvester and Coxeter.  It has some cute
relationships to the icosahedron.  I will send you (and anyone else
who wants) what I have about this.

Technical Details

Message-ID: <1992Sep28.233051.19146@galois.mit.edu>

Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet

References: <1992Sep28.201204.13907@tamsun.tamu.edu>

Show Full Headers

Complete Article Headers

Newsgroups: sci.math.research
Path: arc1-ca.pugleaf.net!sparky!uunet!spool.mu.edu!uwm.edu!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
From: "John C. Baez" <jbaez@BOURBAKI.MIT.EDU>
Subject: Re: Complete Groups / S_6
References: <1992Sep28.201204.13907@tamsun.tamu.edu>
Nntp-Posting-Host: riesz
Message-ID: <1992Sep28.233051.19146@galois.mit.edu>
Sender: Daniel Grayson <dan@math.uiuc.edu>
X-Submissions-To: sci-math-research@uiuc.edu
Organization: MIT Department of Mathematics, Cambridge, MA
X-Administrivia-To: sci-math-research-request@uiuc.edu
Approved: Daniel Grayson <dan@math.uiuc.edu>
Date: Mon, 28 Sep 1992 23:30:51 GMT
Lines: 14

Reply to Parent Message