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

Fuente: arXiv
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Main Authors: Margolis, Leo, Sakurai, Taro
Format: Preprint
Published: 2026
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author Margolis, Leo
Sakurai, Taro
author_facet Margolis, Leo
Sakurai, Taro
contents 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 $G \cong H$.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18220
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Geometric approach to the modular isomorphism problem: groups of order 64
Margolis, Leo
Sakurai, Taro
Group Theory
Commutative Algebra
Rings and Algebras
20C05, 16S34, 20D15, 13P25, 16Z05
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 $G \cong H$.
title Geometric approach to the modular isomorphism problem: groups of order 64
topic Group Theory
Commutative Algebra
Rings and Algebras
20C05, 16S34, 20D15, 13P25, 16Z05
url https://arxiv.org/abs/2603.18220