Complete Isocategorical Classification of Groups of Order 64 via GAP

Fuente: arXiv
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Main Author: Sato, Shoki
Format: Preprint
Published: 2026
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author Sato, Shoki
author_facet Sato, Shoki
contents The classification of finite groups under monoidal equivalence is a fundamental topic in the study of finite quantum groups. While a complete classification has been established for all groups of order strictly less than 64, the case for order 64 has remained limited to the construction of specific examples. In this study, we achieve the complete classification for groups of order 64 by developing an original computational approach using GAP. We describe our methodology and demonstrate that there exist exactly two pairs of non-isomorphic isocategorical groups of this order.
format Preprint
id arxiv_https___arxiv_org_abs_2604_17462
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Complete Isocategorical Classification of Groups of Order 64 via GAP
Sato, Shoki
Group Theory
Quantum Algebra
The classification of finite groups under monoidal equivalence is a fundamental topic in the study of finite quantum groups. While a complete classification has been established for all groups of order strictly less than 64, the case for order 64 has remained limited to the construction of specific examples. In this study, we achieve the complete classification for groups of order 64 by developing an original computational approach using GAP. We describe our methodology and demonstrate that there exist exactly two pairs of non-isomorphic isocategorical groups of this order.
title Complete Isocategorical Classification of Groups of Order 64 via GAP
topic Group Theory
Quantum Algebra
url https://arxiv.org/abs/2604.17462