Brou\'e's Conjecture for 2-blocks with elementary abelian defect groups of order 32

Benjamin Sambale; Cesare G. Ardito

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arxiv 2011.06793 v1 pith:2JHIHS2Y submitted 2020-11-13 math.RT math.GR

Brou\'e's Conjecture for 2-blocks with elementary abelian defect groups of order 32

Cesare G. Ardito , Benjamin Sambale This is my paper

classification math.RT math.GR

keywords defectabeliangroupsblocksbroucasesconjectureelementary

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The first author has recently classified the Morita equivalence classes of 2-blocks B of finite groups with elementary abelian defect group of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of B. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Brou\'e's Abelian Defect Group Conjecture in this situation.

Brou\'e's Conjecture for 2-blocks with elementary abelian defect groups of order 32

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