Local control in fusion systems of \(p\)-blocks of finite groups.
The authors prove a block theoretic analogue of Glauberman's \(ZJ\)-theorem: If \(p\) is an odd prime, \(b\) a \(p\)-block of a finite group \(G\) such that \(\text{SL}(2,p)\) is not involved in \(N_G(Q,e)/C_G(Q)\) for any \(b\)-subpair \((Q,e)\), then \(N_G(Z(J(P)))\) controls \(b\)-fusion, where \(P\) is a defect group of \(b\) and \(J(P)\) denotes the Thompson subgroup of \(P\). Several results of general interest about fusion and blocks are also included in the paper.
scientific article; zbMATH DE number 1868069