The Relevance of Group Theory to Composing Peals of Plain Bob Triples
Loading...
Authors
Mikkelson, Rana
Issue Date
2004
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
Change Ringing is the art of ringing tower or hand bells according to a specific
set of rules defined by the British in the 1600s. In particular we examine
the group structure in peals of a method called Plain Bob Triples, which
are composed of permutations of the hells. This gives us one application of
group theory; the symmetric group on n letters or, here, n bells. In this paper
we will examine what group structure can be found in a peal of Plain Bob
Thiples. We also discuss how peals are composed by factoring the symmetric
group on n letters so that the task of testing for repeated permutations is
reduced to working in cosets.
We show that not only do the lead heads of a peal not have to form a
group, they never do. This is a result based almost entirely on the order of
the group of lead heads and the fact that the group A 6 is the only subgroup
of S 6 with order 360. We also show that the set of leads is the same as the
group S 6. Finally we show, as a part of explaining how peals are composed
in parts we do a proof to explain why we can be assured of having all the
elements of a particular coset if we have just one of them. Finally we discuss
two peals whose structure suggests that they are peals composed in parts like
most peals, but looks are deceiving, and we find out that they are actually
constructed using a very different procedure.
Description
iv, 30 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.