The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B....The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B. Recently, the inductive blockwise Alperin weight condition has been introduced such that the blockwise Alperin weight conjecture holds if all non-abelian simple groups satisfy these conditions. We will verify the inductive blockwise Alperin weight condition for the finite simple groups PSL（3, q） in this paper.展开更多
Let G be a finite group and ι be any prime dividing|G|.The blockwise Alperin weight conjeeture states that the number of the irreducible Brauer characters in an E-block B of G equals the number of the G-conjugacy cla...Let G be a finite group and ι be any prime dividing|G|.The blockwise Alperin weight conjeeture states that the number of the irreducible Brauer characters in an E-block B of G equals the number of the G-conjugacy classes of ι-weights belonging to B.Recently,this conjeeture has been reduced to the simple groups,which means that to prove the blockwise Alperin weight conjeeture,it suffices to prove that all non-abelian simple groups satisfy the inductive blockwise Alperin weight condition.In this paper,we verify this inductive cond计ion for the finite simple groups PSp4(g)and non-defining characteristic,where q is a power of an odd prime.展开更多
In this paper, we shall mainly study the p-solvable finite group in terms of p-local rank, and a group theoretic characterization will be given of finite p-solvable groups with p-local rank two.Theorem A Let G be a fi...In this paper, we shall mainly study the p-solvable finite group in terms of p-local rank, and a group theoretic characterization will be given of finite p-solvable groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G) = 2 and Op(G) = 1. If P is a Sylow p-subgroup of G, then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G) = 1. Then the p-length lp(G) < plr(G); if in addition plr(G) = 1p(G) and p > 5 is odd, then plr(G) = 0 or 1.展开更多
文摘The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B. Recently, the inductive blockwise Alperin weight condition has been introduced such that the blockwise Alperin weight conjecture holds if all non-abelian simple groups satisfy these conditions. We will verify the inductive blockwise Alperin weight condition for the finite simple groups PSL（3, q） in this paper.
基金This work was supported by the Fundamental Research Funds for the Central Universities(No.2682019CX48)the National Natural Science Foundation of China(No.11631001).
文摘Let G be a finite group and ι be any prime dividing|G|.The blockwise Alperin weight conjeeture states that the number of the irreducible Brauer characters in an E-block B of G equals the number of the G-conjugacy classes of ι-weights belonging to B.Recently,this conjeeture has been reduced to the simple groups,which means that to prove the blockwise Alperin weight conjeeture,it suffices to prove that all non-abelian simple groups satisfy the inductive blockwise Alperin weight condition.In this paper,we verify this inductive cond计ion for the finite simple groups PSp4(g)and non-defining characteristic,where q is a power of an odd prime.
文摘In this paper, we shall mainly study the p-solvable finite group in terms of p-local rank, and a group theoretic characterization will be given of finite p-solvable groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G) = 2 and Op(G) = 1. If P is a Sylow p-subgroup of G, then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G) = 1. Then the p-length lp(G) < plr(G); if in addition plr(G) = 1p(G) and p > 5 is odd, then plr(G) = 0 or 1.
