# [r-t] Ringable Alternating Groups On Five Bells

Alexander Holroyd holroyd at math.ubc.ca
Sat Aug 29 17:00:17 BST 2020

```A fair bit of this was discussed in 2004.  (You have to dig a bit):

https://lists.ringingworld.co.uk/pipermail/ringing-theory/2004-September/012732.html

https://lists.ringingworld.co.uk/pipermail/ringing-theory/2004-September/019463.html

https://lists.ringingworld.co.uk/pipermail/ringing-theory/2004-September/019473.html

https://lists.ringingworld.co.uk/pipermail/ringing-theory/2004-September/019486.html

On 29/08/2020 00:26, Richard Pullin wrote:
> This is really interesting and useful, thanks for sharing.
>
> As the alternating group on 5 is isomorphic to Hudson's group, it
> would be interesting to see which of these blocks can be turned into
> Hudson type components for Minor methods and principles. For example,
> the Doubles six: 3.1.3.1.3.1 can be replaced by 34.1.34.1.34.1 in
> Minor, which is a very easy-to-see demonstration of the (123) cycles
> being replaced by (123)(456) cycles. I'm sure the idea of using A_5 in
> this way will have occurred to others, but they may have been put off
> by the tendency of 3/4-blow places in the resulting Minor methods.
>
> If you arbitrarily try this on a bobbed lead of Grandsire Doubles, one
> result is: 34.1.5.1.34.1,2 (which perhaps closer resembles Double
> Grandsire Doubles with bobs at the half lead and lead end.) The
> method's plain course is Hudson's group, so the trick has worked. As
> the half lead rows are the same as in Cambridge S and Oxford TB, you
> can get a number of variants by replacing the half lead with 5 and/or
> the lead head with 1. I was then reminded that one of these variants
> had already been devised a few months ago by the mathematician Robert
> A Wilson (though his method has the tenor as hunt bell, so I rotated it.)
>
> We can go a step further and turn this into a challenging Principle
> with 360 changes in the plain course, though some might prefer to
> think of it as a variable-treble touch of the Plain method:
> https://complib.org/method/39339?accessKey=b9d3f9ca822c8bd08bdc2248ec151b4e5c89b0
> <https://complib.org/method/39339?accessKey=b9d3f9ca822c8bd08bdc2248ec151b4e5c89b0> For
> a 720 you simply use two singles a course apart:
> https://complib.org/composition/70150?accessKey=4222c763a30983fab67f274873ab5552ffe14201
> <https://complib.org/composition/70150?accessKey=4222c763a30983fab67f274873ab5552ffe14201>
>
> I love how this extent is analogous to a 2-single 120 of Stedman
> Doubles, which brings us right back to the original topic of A_5.
>
> So what else can be done with the Doubles blocks?
>
> _______________________________________________
> ringing-theory mailing list
> ringing-theory at bellringers.org
> https://bellringers.org/listinfo/ringing-theory
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://bellringers.org/pipermail/ringing-theory/attachments/20200829/9f7bebc4/attachment.html>
```