Finite p-subgroups of Sp(n)

Date
2021-09
Advisor
Ünlü, Özgün
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Bilkent University
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Language
English
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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.

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Keywords
p-group, Symplectic group
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Published Version (Please cite this version)