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      Finite p-subgroups of Sp(n)

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      Author(s)
      Çetin, Mustafa Seyyid
      Advisor
      Ünlü, Özgün
      Date
      2021-09
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
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      Abstract
      Hikari [1] classifies all finite p-subgroups of simple algebras, and Banieqbal [2] classi-fies the finite subgroups of 2×2 matrices over a division algebra of characteristic zero. In this thesis, we give a new proof for the classification of the finite p-subgroups of 2 × 2 matrices over the quaternionic algebra. Using this classification, we classify fi-nite p-subgroups of the symplectic group Sp(2). More precisely, for every prime p, we define a denumerable family of p-subgroups of Sp(2) so that every finite p-subgroup of Sp(2) lives inside one of the members of this family. To give this classification, we proved general results for Sp(n) whenever possible.
      Keywords
      p-group
      Symplectic group
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      http://hdl.handle.net/11693/76534
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      • Dept. of Mathematics - Master's degree 128
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