Block-diagonality of LFS-groups of p-type

In this paper, we prove that every locally finite simple group of p-type has a Kegel cover K={(Hi,Mi)|i∈I} such that•Hi/Op(Hi) is the central product of perfect central extensions of classical groups defined over a field in characteristic p;•if (H1,M1),(H2,M2)∈K with H1⩽H2 then H2 is ‘block-diagonal’ for H1.Roughly speaking, ‘H2 is block-diagonal for H1’ means that for every component L2 of H2/Op(H2) and every non-trivial composition factor C for H1 on L2 there is exactly one component L1 of H1/Op(H1) that is not trivial on L2. Moreover C is a natural module for L1. The exact definition of block-diagonal is given in Section 4.