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- W2912605501 abstract "Let $N$ be a normal subgroup of a finite group $G$. In this paper, we consider the elements $g$ of $N$ such that $chi(g)neq 0$ for all irreducible characters $chi$ of $G$. Such an element is said to be non-vanishing in $G$. Let $p$ be a prime. If all $p$-elements of $N$ satisfy the previous property, then we prove that $N$ has a normal Sylow $p$-subgroup. As a consequence, we also study certain arithmetical properties of the $G$-conjugacy class sizes of the elements of $N$ which are zeros of some irreducible character of $G$. In particular, if $N=G$, then new contributions are obtained." @default.
- W2912605501 created "2019-02-21" @default.
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- W2912605501 date "2019-02-08" @default.
- W2912605501 modified "2023-10-18" @default.
- W2912605501 title "On zeros of irreducible characters lying in a normal subgroup" @default.
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- W2912605501 doi "https://doi.org/10.48550/arxiv.1902.03170" @default.
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