Clifford theory of characters in induced blocks
Clifford theory of characters in induced blocks
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DOI：
10.1090/proc/12431
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发表时间：
2013-10
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影响因子：
--
通讯作者：
Shigeo Koshitani;Britta Spaeth
中科院分区：
文献类型：
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作者：
Shigeo Koshitani;Britta Spaeth
我们给出了一个新的判定有限群的特征标是否扩张的准则。设G是有限群，p是素数.对于N ∈ G，我们分别考虑N和NN（D）的p-块B和B，其中（B）= B，其中D是B的亏群。在假设G与G的正规子群G[B]重合的条件下，给出了φ的所有不可约分支集与（φ′）NG（D）的所有不可约分支集之间的特征标对应，其中φ和φ分别是B和B中的不可约Brauer特征标.这意味着Harris-Knorr定理的一种推广。一个重要的工具是某些扩展的存在，这些扩展也有助于检查归纳Alperin-McKay和归纳Bessel Alperin Weight条件。
We present a new criterion to predict if a character of a finite group extends. Let G be a finite group and p a prime. For N ⊳G, we consider p-blocks b and b of N and NN (D), respectively, with (b ) = b, where D is a defect group of b. Under the assumption that G coincides with a normal subgroup G[b] of G, which was introduced by Dade early 1970’s, we give a character correspondence between the sets of all irreducible constituents of φ and those of (φ′)NG(D) where φ and φ are irreducible Brauer characters in b and b, respectively. This implies a sort of generalization of the theorem of Harris-Knorr. An important tool is the existence of certain extensions that also helps in checking the inductive Alperin-McKay and inductive Blockwise Alperin Weight conditions, due to the second author.