The Atiyah Conjecture originates from a paper written 40 years ago by Sir Michael Atiyah, a famous mathematician and Fields medalist. Since publication of the paper, mathematicians have been working to solve many questions related to the conjecture, but it is still open.
The conjecture is about certain topological invariants attached to a group ๐บ. There are examples showing that the conjecture does not hold in general. These examples involve something like the lamplighter group (the wreath product โค/2โค โ โค). We are interested in looking at examples where this is not the case. We are interested in the specific case where ๐บ is a finitely generated group in which the Prรผfer group can be embedded as the center. The Prรผfer group is a ๐-group for some prime ๐ and its finite subgroups have unbounded order, in particular the finite subgroups of G will have unbounded order.
To understand whether any form of the Atiyah conjecture is true for ๐บ, it will first help to determine whether the group ring ๐๐บ of the group ๐บ has a classical ring of quotients for some field ๐. To determine this we will need to know the zero divisors for the group ring ๐๐บ. Our investigations will be divided into two cases, namely when the characteristic of the field ๐ is the same as the prime p for the Prรผfer group and when it is different. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/52949 |
| Date | 15 June 2015 |
| Creators | Welch, Amanda Renee |
| Contributors | Mathematics, Linnell, Peter A., Rossi, John F., Floyd, William J., Brown, Ezra A. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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