Perfect isometries for blocks with abelian defect groups and dihedral inertial quotients of order \(6\)
Let \(b\) be a block of a finite group \(G\) with abelian defect group \(P\). A conjecture by M. Broué says that \(b\) is isotypic to its Brauer correspondent \(c\) in \(N_G(P)\). The author verifies this conjecture in the special case where the inertial quotient \(N_G(P, e)/PC_G(P)\) is dihedral of order 6; here \(e\) denotes a block of \(C_G(P)\) such that \(e^G = b\). In previous papers, some of them joint with L. Puig, the author had proved a similar result for the case \(|N_G(P,e)/PC_G(P) |\leq 4\).
scientific article; zbMATH DE number 763909