# [r-t] Hudson stuff

Richard Smith richard at ex-parrot.com
Thu Sep 16 11:02:33 UTC 2004

```Philip Saddleton wrote:

> Really? I'd have thought that most worthwhile groups couldn't be
> generated from changes - or are you restricting yourself to those that
> can?

I don't know exactly what you mean by "worthwhile", but all
of the larger subgroups of S_6 (upto conjugation)  can be
generated by changes:

[6.01] = <-,1,4>    (Order 720m)
[6.02] = <1,2,3>    (Order 360p)
[6.03] = <-,3,4>    (Order 120m)
[6.04] = <-,1,23>   (Order  72m)
[6.05] = <1,2,34>   (Order  60p)
[6.06] = <-,1,34>   (Order  48m)

where [6.0x] is the name given to the group in Brian Price's
paper.

The smaller transitive groups, on the other hand, tend to be
harder to generate.  Of the groups [6.07] through [6.16]
only the dihedral group, [6.13], can be generated using only
changes.

We have examples of methods that generate [6.03] (Striking),
[6.05] (Ander's slightly inelegant Hudson's principle),
[6.06] (Kidderminster) and [6.13] (Original).  [6.01] and
[6.02] are too big to be interesting.  This leaves [6.04].
Can anyone find an example of this?  The group contains a
6-cycle, so a principle seems plausible.

Richard

```