CEU Electronic Theses and Dissertations, 2013
| Author | Andrus, Ivan Ben |
|---|---|
| Title | Transposable Character Tables |
| Summary | In the study of finite groups a sort of duality has been observed between conjugacy classes and irreducible characters, but the connection is quite murky. Abelian groups are special in that, as Z-modules, they have true duals. They also have the property that the transpose of their character tables is still a character table. We generalize this by allowing rows to be multiplied by constants before and after transposition. A group whose character table is still a character table after this generalized transposition is called transposable. Transposable groups generalize slightly the notion of self-dual groups of Okuyama and Hanaki. We derive some properties of transposable groups and give some examples. We also study the related property of having square conjugacy class sizes and show that no non-abelian simple group has square class sizes. |
| Supervisor | Hegedűs, Pál |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2013/andrus_ivan.pdf |
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