Basic Morita Equivalences And Weights In Blocks

Weights are defined by local subgroups of finite groups.The famous Alperin weight conjecture claims that the number of isomorphism classes of simple modules in any(p-)block equals the number of weights in this block.The conception of basic Morita equivalences is due to L.Puig and it preserves some local information of blocks.In this thesis,we prove that if two blocks of finite groups are basically Morita equivalent,they have the same number of the weight of conjugate class.