Zeros of characters of finite groups
Zeros of characters of finite groups
复制标题
DOI：
10.1515/jgth.2000.028
复制
发表时间：
2000-01
影响因子：
0.5
通讯作者：
G. Malle;G. Navarro;J. B. Olsson
中科院分区：
文献类型：
--
作者：
G. Malle;G. Navarro;J. B. Olsson
定理A和定理B的一些变体是不成立的。例如，如果Irr(G)中的χ具有可被p整除的度，则不一定存在使χ在其上消失的p元素。考虑任意阶数为10且p = 2的L2（11）就足够了。如果χ在某元素x上消失，则χ在x的某p部分上消失也是不成立的。例如，如果G是M11，则χ具有11次的不可约性质，在6阶元素上消失，并且在2元和3元上非零。第三，在任何四元数群中，非线性特征在素数阶元素上不存在。有趣的是，这似乎是简单群体的情况（我们确实对李氏型群体和零星群体证明了这一点）。
There are some variations of theorems A and B which are simply not true. For instance, if χ in Irr(G) has degree divisible by p, then there does not necessarily exist a p-element on which χ vanishes. It is enough to consider L2(11) with any character of degree 10 and p = 2. It is also not true that if χ vanishes on some element x, then χ has to vanish on some p-part of x. For instance, if G is M11, then χ has an irreducible character of degree 11, vanishing on an element of order 6 and which is nonzero on 2and 3-elements. Thirdly, it is not true that a nonlinear character has to vanish on some element of prime order, as shown by any quaternion group. Interestingly enough, this seems to be the case for simple groups (and we do prove this for the groups of Lie type and the sporadic groups).