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A note on blocks of finite groups with TI Sylow p-subgroups

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Abstract

Let \(\mathbb {F}\) be an algebraically closed field of characteristic zero. We prove that functorial equivalence over \(\mathbb {F}\) and perfect isometry between blocks of finite groups do not imply each other.

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References

  1. Broué, M.: Isométries parfaites, types de blocs, catégories dérivées. Astérisque No. 181–182, 61–92 (1990)

    Google Scholar 

  2. Blau, H.I., Michler, G.O.: Modular representation theory of finite groups with T.I. Sylow \(p\)-subgroups. Trans. Amer. Math. Soc. 319(2), 417–468 (1990)

    MathSciNet  Google Scholar 

  3. Boltje, R., Perepelitsky, P.: \(p\)-permutation equivalences between blocks of group algebras. arXiv:2007.09253 (2020)

  4. Boltje, R., Xu, B.: On \(p\)-permutation equivalences: between Rickard equivalences and isotypies. Trans. Amer. Math. Soc. 360(10), 5067–5087 (2008)

    Article  MathSciNet  Google Scholar 

  5. Bouc, S., Yılmaz, D.: Diagonal \(p\)-permutation functors, semisimplicity, and functorial equivalence of blocks. Adv. Math. 411, Paper No. 108799, 54 pp. (2022)

  6. bibitemBoucYilmaz2023 Bouc, S., Yılmaz, D.: Stable functorial equivalence of blocks. arXiv:2303.06976 (2023)

  7. Cliff, G.: On centers of \(2\)-blocks of Suzuki groups. J. Algebra 226, 74–90 (2000)

    Article  MathSciNet  Google Scholar 

  8. Linckelmann, M.: The Block Theory of Finite Group Algebras. Vol. II. London Mathematical Society Student Texts, 92. Cambridge University Press, Cambridge (2018)

  9. Robinson, G.R.: A note on perfect isometries. J. Algebra 226, 71–73 (2000)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was supported by the BAGEP Award of the Science Academy.

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  1. Department of Mathematics, Bilkent University, 06800, Ankara, Turkey

    Deniz Yılmaz

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  1. Deniz Yılmaz
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Correspondence to Deniz Yılmaz.

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Yılmaz, D. A note on blocks of finite groups with TI Sylow p-subgroups. Arch. Math. 122, 355–357 (2024). https://doi.org/10.1007/s00013-024-01968-0

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  • DOI: https://doi.org/10.1007/s00013-024-01968-0

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