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arXiv · 2406.01810

The Modular Isomorphism Problem -- the alternative perspective on counterexamples

Czesław Bagiński·Kamil Zabielski
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Abstract

As a result of impressive research arXiv:2106.07231, D. Garc\'{\i}a-Lucas, \'{A}. del R\'{i}o and L. Margolis defined an infinite series of non-isomorphic $2$-groups $G$ and $H$, whose group algebras $\mathbb{F}G$ and $\mathbb{F}H$ over the field $\mathbb{F}=\mathbb{F}_2$ are isomorphic, solving negatively the long-standing Modular Isomorphism Problem (MIP). In this note we give a different perspective on their examples and show that they are special cases of a more general construction. We also show that this type of construction for $p>2$ does not provide a similar counterexample to the MIP.

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Czesław Bagiński, Kamil Zabielski. 2024-06-03. The Modular Isomorphism Problem -- the alternative perspective on counterexamples. https://arxiv.org/abs/2406.01810

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