# [r-t] Minor principles

Fri Sep 3 18:47:13 UTC 2004

```Philip Saddleton <pabs at cantab.net> wrote at 23:12:39 on Tue, 31 Aug 2004
>A group of order 36 - the even rows with 1,5,6 either in 1,5,6 or
>2,3,4. The leads starting with these are mutually true, leaving another
>12 cosets.

There are 3 possibilities that allow the lead end to be included as
well:

1,2,3 in 1,2,3 or 4,5,6 (even)
1,4,5 in 1,4,5 or 2,3,6 (even)
1,2,3 in 1,2,3 (even) or (1,2,3) odd

>A group of order 20 (isomorphic to the Thurstans part-ends), with 5
>fixed, generated by 134652 & 432156. Two leads starting from each
>element, plus another 20 cosets.

This is the only possibility.

I don't think that it is possible to avoid multiple blows in one place.
You may think that these are improvements - I don't know how they are
best described:

-36-34.16.34-56.16-1234-12-16.14-16-1236

23456   1  2  4
---------------
23564   -  -  -
32654      -  -
32546   -  -  -
---------------
Repeat
-=1456

-36-34.16.34-56-36-34.16.34-56.1236.1234.34.1256.36-34-14-34-56.36.16-123
4-16.56

123456  5
---------
241356  -
---------
4-part
-=1456

--
Regards
Philip