Broué's conjecture for non-principal 3-blocks of finite groups
Let \(G\) be the O'Nan finite simple group of order \(2^9\cdot 3^4\cdot 5\cdot 7^3\cdot 11\cdot 19\cdot 31\), and let \(A\) be the (non-principal) 3-block of \(G\) with elementary Abelian defect group \(D\) of order 9. The authors show that \(A\) is splendidly equivalent to its Brauer correspondent in \(N_G(D)\) and Puig equivalent to the principal 3-block of \(\text{PSL}(3,4)\). This verifies Broué's Abelian defect group conjecture for this block of \(G\). The authors also deal with the non-principal 3-block of maximal defect in the Higman-Sims finite simple group of order \(2^9\cdot 3^2\cdot 5^3\cdot 7 \cdot 11\) in a similar way.
scientific article; zbMATH DE number 1787490
scientific article