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<p>The Modular Isomorphism Problem asks, if an isomorphism between modular group algebras of finite <i>p</i>-groups over a field <i>F</i> implies an isomorphism of the group bases. We explore the differences of knowledge on the problem when <i>F</i> is either assumed to be a prime field or a general field of characteristic&#xa0;<i>p</i>. After revising the literature and explaining reasons for the differences, we generalize some of the positive answers to the problem from the prime field case to the general case.</p>

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The modular isomorphism problem over all fields

  • 期刊论文

  • 发表日期：

    2025年11月17日

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  • Leo Margolis,
  • Taro Sakurai

摘要

The Modular Isomorphism Problem asks, if an isomorphism between modular group algebras of finite p-groups over a field F implies an isomorphism of the group bases. We explore the differences of knowledge on the problem when F is either assumed to be a prime field or a general field of characteristic p. After revising the literature and explaining reasons for the differences, we generalize some of the positive answers to the problem from the prime field case to the general case.