CEU Electronic Theses and Dissertations, 2022
| Author | Szabó, Dávid |
|---|---|
| Title | Jordan Type Problems via Class 2 Nilpotent and Twisted Heisenberg Groups |
| Summary | We investigate the structure of finitely generated nilpotent groups of class at most 2 and show an explicit way to construct all such groups starting from cyclic groups and 2- generated nilpotent groups of class 2 by applying the operations of central and subdirect products. Using this description, we show that every finitely generated nilpotent group of class at most 2 is isomorphic to a subgroup of a generalisation of the Heisenberg group. Using these results we prove the main statements of the thesis. We show the existence of an algebraic variety and a smooth manifold on which every finite nilpotent group of class at most 2 of bounded rank acts faithfully via birational automorphisms and via diffeomorphisms, respectively. This gives a sharp answer to a Jordan type problem about the birational automorphism groups and answers a question of Mundet i Riera in the smooth case. |
| Supervisor | Pyber, László |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2022/szabo_david.pdf |
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