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On a new construction in group theory
- Publication Year :
- 2011
- Publisher :
- Queen Mary, University of London, 2011.
-
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.
- Subjects :
- 510
Mathematics
Subjects
Details
- Language :
- English
- Database :
- British Library EThOS
- Publication Type :
- Dissertation/ Thesis
- Accession number :
- edsble.542021
- Document Type :
- Electronic Thesis or Dissertation