The Mathieu group \sf M₁₂ vs SL₃(3) in characteristic 3

2026/07/17 by Shigeo Koshitani, Tetsuro Okuyama
Mathematics · #math.RT #math.RA

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Abstract

We prove that the principal 3-blocks of the Mathieu group \sf M₁₂ and the special linear group \SL₃(3) are splendidly Rickard equivalent, and hence derived equivalent, by applying Rickard's theorem whose origin goes back to the second author. As a byproduct we answer to a question on the first Hochschild cohomology of the principal 3-blocks above posed by W. Murphy.

Citations

• The local structure of finite groups of characteristic 2 type

Related

• A remark on Rickard complexes
• The Structure of the Three-Dimensional Special Linear Group over a Local Field
• Derived Reid's recipe for abelian subgroups of SL3(C)
• Singular blocks of restricted sl3
• Galois descent of splendid Rickard equivalences for blocks of p-nilpotent groups