RESEARCH ANNOUNCEMENTS Local Characterizations of Block Covers and Their Applications

Let G be a finite group,H≤G,F a field of characteristic p,where p is afixed prime;B=e·FH and B=e·FG be an FH-block and an FG-block resp.B issaid to be covered by B if B|B↓_(H×H);dually,B is said to be covered by B ifB|B↑~(G×G).Donote the Brauer homomorphism into C_G(P)by Br_(C_G(P))for any p-subgroupP.