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arXiv · 2506.03446

Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent

John Revere McHugh
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Abstract

We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation equivalent. These results help to clarify the distinction between a $p$-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a $p$-permutation equivalence.

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John Revere McHugh. 2025-06-03. Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent. https://arxiv.org/abs/2506.03446

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