dc.description.abstract | My supervisors Ian Chiswell and Thomas M¨uller have found a new class of
groups of functions defined on intervals of the real line, with multiplication
defined by analogy with multiplication in free groups. I have extended this idea
to functions defined on a densely ordered abelian group. This doesn’t give rise
to a class of groups straight away, but using the idea of exponentiation from a
paper by Myasnikov, Remeslennikov and Serbin, I have formed another class of
groups, in which each group contains a subgroup isomorphic to one of Chiswell
and M¨uller’s groups.
After the introduction, the second chapter defines the set that contains the
group and describes the multiplication for elements within the set. In chapter
three I define exponentiation, which leads on to chapter four, in which I describe
how it is used to find my groups. Then in chapter five I describe the structure
of the centralisers of certain elements within the groups. | en_US |