Quasi-projective Brauer characters
Quasi-projective Brauer characters
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DOI：
10.1016/j.jalgebra.2017.12.016
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发表时间：
2017-12
影响因子：
0.9
通讯作者：
Yanjun Liu;W. Willems
中科院分区：
文献类型：
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作者：
Yanjun Liu;W. Willems
研究了有限群G的p-Brauer特征标，它是有限群G的广义特征标在p-奇异元上为零的限制条件，其中p是固定素数，且p整除群G的阶。这种Brauer特征标称为拟投射特征标。我们证明了对于每个不可约Brauer特征标φ，存在一个极小p-幂，比如pa（φ），使得pa（φ）φ是拟投射的.指数a（φ）仅取决于φ所属块的Cartan矩阵。此外，p a（φ）由提供φ的模的顶点有界，并且等式在G是p-可解的情况下成立。我们给出了猜想a（φ）= 0发生的一些证据，当且仅当φ属于亏为0的块.最后，我们研究了块B的不可分解拟投射Brauer特征标.这个集合是有限的，对应于由B的Cartan矩阵定义的有理锥的最小Hilbert基。
We study p-Brauer characters of a finite group G which are restrictions of generalized characters vanishing on p-singular elements for a fixed prime p dividing the order of G. Such Brauer characters are called quasi-projective. We show that for each irreducible Brauer character φ there exists a minimal p-power, say p a (φ), such that p a (φ) φ is quasi-projective. The exponent a (φ) only depends on the Cartan matrix of the block to which φ belongs. Moreover p a (φ) is bounded by the vertex of the module affording φ, and equality holds in case that G is p-solvable. We give some evidence for the conjecture that a (φ)= 0 occurs if and only if φ belongs to a block of defect 0. Finally, we study indecomposable quasi-projective Brauer characters of a block B. This set is finite and corresponds to a minimal Hilbert basis of the rational cone defined by the Cartan matrix of B.