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arXiv · 2512.20341

Unipotent orbits of elements in a quaternion ring of odd order

David Dolžan
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Abstract

Let $n \in \NN$ and let $q=p^r$ be an odd prime power. Let $R$ be a finite commutative local principal ring of cardinality $q^{n}$ with $R/J(R) \simeq GF(q)$. We study the conjugation action of the group of all unipotent elements in the quaternion ring $H(R)$ on $H(R)$ and we classify the resulting unipotent similarity classes, using a reduction to the ring of $2$-by-$2$ matrices over $R$.

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David Dolžan. 2025-12-23. Unipotent orbits of elements in a quaternion ring of odd order. https://arxiv.org/abs/2512.20341

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