An elementary classification of the quaternionic reflection groups of rank two
Shayne Waldron
Abstract:
We give an elementary classification and presentation of the finite quaternionic
reflection groups of rank two, based on the notion of a “reflection system”. This
simplifies the existing classification, which is shown to be incomplete, e.g., there
exist four imprimitive quaternionic reflection groups of order 192 with 22 reflections
which are not isomorphic (one of which was previously unknown).
Keywords:
imprimitive quaternionic reflection groups, reflection systems, symplectic
group, binary polyhedral groups, dicyclic groups, finite collineation groups, representations over the quaternions, Frobenius-Schur indicator.
Math Review Classification:
Primary 05B30, 15B33, 20C25, 20G20, 51M05, 51M20;
Secondary 15B57, 51E99, 51M15, 65D30.
Length: 35 Pages
Last Updated: 2 September 2025
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