From: huw@eryr.adar.net (Huw Davies)
Subject: Re: Paper by J.A.Todd on "The odd number 6"
Date: 5 Feb 1999 05:19:40 GMT
Newsgroups: sci.math
Keywords: Group theory, Galois theory

On Fri, 05 Feb 1999 00:05:34 GMT, 
  torquemada@my-dejanews.com <torquemada@my-dejanews.com> wrote:
>In article <79999v$h2t$1@newsflash.concordia.ca>,
>  mckay@cs.concordia.ca (MCKAY john) wrote:
>
>> Not only did Todd lecture on this topic but he wrote a paper
>> on it. Perhaps someone can tell us more of its content?
>
>Let me second that!
>
>Is that Todd as in Todd class and Todd genus?
>--
yes. Also the Todd-Coxeter algorithm, Shepherd&Todd's classification
of finite complex reflexion groups, and cute stuff about Matthieu
groups ...

The odd number 6 paper is Math. Proc. Camb. Phil. Soc. 41 (1945) 66--68 
I don't have easy access to this, but Math. Review 6 (1945) 198, 
has a review which indicates that it about special properties
of the symmetric group on 6 letters, though it is couched in terms of
`classical' Galois theory, i.e. it talks about functions of the roots
of a polynomial and the number of different values you get when you
permute the roots. It looks like the property of interest is the
fact that S_6 has two conjugacy classes of subgroups of index 6,
whereas every other S_n has a unique class of subgroups of index n,
rather than the outer automorphism (of course, these aren't entirely
unconnected facts).

Huw