Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Cesare Giulio Ardito

doi:10.1016/j.jalgebra.2020.12.036

Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Representation Theory 2021-01-25 v4 Group Theory

Authors: Cesare Giulio Ardito

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Abstract

We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

Keywords

morita equivalence blocks of finite groups elementary abelian defect groups discrete valuation ring harada conjecture

Cite

@article{arxiv.1908.02652,
  title  = {Morita equivalence classes of blocks with elementary abelian defect groups of order 32},
  author = {Cesare Giulio Ardito},
  journal= {arXiv preprint arXiv:1908.02652},
  year   = {2021}
}

Comments

32 pages. Removed Prop. 5.4 due to an incomplete proof (the result will appear in a subsequent paper)

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