Morita equivalence classes of tame blocks of finite groups

Norman Macgregor

doi:10.1016/j.jalgebra.2022.06.014

Morita equivalence classes of tame blocks of finite groups

Norman Macgregor

Mathematics

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Abstract

We show that several Morita equivalence classes of tame algebras do not occur as blocks of finite groups. This refines classifications by Erdmann of classes of blocks with dihedral, semidihedral, and generalised quaternion defect groups. In particular we now have a complete classification of the Morita equivalence classes of blocks of finite groups with dihedral defect groups.

Original language	English
Pages (from-to)	719-754
Journal	Journal of Algebra
Volume	608
Early online date	4 Jul 2022
DOIs	https://doi.org/10.1016/j.jalgebra.2022.06.014
Publication status	Published - 1 Oct 2022

Keywords

Block
Defect group
Morita equivalence
Quasi-simple
Tame algebra

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https://linkinghub.elsevier.com/retrieve/pii/S0021869322003064

Cite this

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AB - We show that several Morita equivalence classes of tame algebras do not occur as blocks of finite groups. This refines classifications by Erdmann of classes of blocks with dihedral, semidihedral, and generalised quaternion defect groups. In particular we now have a complete classification of the Morita equivalence classes of blocks of finite groups with dihedral defect groups.

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ER -

Morita equivalence classes of tame blocks of finite groups

Abstract

Keywords

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