论文标题
角色表和缺陷组
Character tables and defect groups
论文作者
论文摘要
令B为具有缺陷组的有限组G的块。我们证明D的中心的指数由G的字符表确定。特别是，当且仅当B包含一个“大型”不可约束的P-Conjugate字符时，我们显示D是循环的。更一般而言，对于Abelian D，我们就字符值获得了D指数的明确公式。在很小的情况下，即使在这种情况下也确定了D的同构类型。此外，它可以从字符表中读取是否| d/d'| = 4，其中d'表示D的换向器子组。我们还根据字符表提出了对nilpotent块的新表征。
Let B be a block of a finite group G with defect group D. We prove that the exponent of the center of D is determined by the character table of G. In particular, we show that D is cyclic if and only if B contains a "large" family of irreducible p-conjugate characters. More generally, for abelian D we obtain an explicit formula for the exponent of D in terms of character values. In small cases even the isomorphism type of D is determined in this situation. Moreover, it can read off from the character table whether |D/D'|=4 where D' denotes the commutator subgroup of D. We also propose a new characterization of nilpotent blocks in terms of the character table.
