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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… Click to show full abstract
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 $n \leq 9$.
Keywords:
characters symmetric;
groups double;
alternating groups;
steinberg characters;
quasi steinberg;
symmetric alternating
Journal Title: Journal of Algebra and Its Applications
Year Published: 2021
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Journal Title: Journal of Algebra and Its Applications
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!