Geometric approach to the modular isomorphism problem: groups of order 64
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917365452636160 |
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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 |