Geometric approach to the modular isomorphism problem: groups of order 64

Leo Margolis; Taro Sakurai

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arXiv · 2603.18220

Geometric approach to the modular isomorphism problem: groups of order 64

Leo Margolis·Taro Sakurai

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Abstract

We introduce a procedure based on computational algebraic geometry to determine whether two algebras are isomorphic. We then apply it to show that if $R$ is a commutative unital ring in which $2$ is not invertible, $G$ is a group of order dividing $64$ and $H$ some group, then an isomorphism of unital algebras $RG \cong RH$ implies an isomorphism of groups $G \cong H$.

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Leo Margolis, Taro Sakurai. 2026-03-18. Geometric approach to the modular isomorphism problem: groups of order 64. https://arxiv.org/abs/2603.18220

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