论文标题
关于对称和交替组的准斯坦伯格字符及其双重封面
On Quasi Steinberg characters of Symmetric and Alternating groups and their Double Covers
论文作者
论文摘要
如果有限的组$ g $的不可约性字符称为prime $ p $的quasi $ p $ -Steinberg字符，如果每$ p $ gular元素为$ g $，则为prime $ p $。在本文中，我们将Symmetric（$ s_n $）和交替（$ a_n $）组及其双重封面的准$ P $ -P $ -Steinberg字符分类。特别是，存在$ s_n $的非线性准准$ P $ -Steinberg字符意味着$ n \ leq 8 $和$ a_n $的$ n \ n \ leq 9 $。
An irreducible character of a finite group $G$ is called quasi $p$-Steinberg character for a prime $p$ if it takes a nonzero value on every $p$-regular element of $G$. In this article, we classify the quasi $p$-Steinberg characters of Symmetric ($S_n$) and Alternating ($A_n$) groups and their double covers. In particular, an existence of a non-linear quasi $p$-Steinberg character of $S_n$ implies $n \leq 8$ and of $A_n$ implies $n \leq 9$.
