Characterization of some finite simple groups by the set of orders of vanishing elements and order

S. Askary

doi:10.37863/umzh.v73i11.1069

S. Askary Imam-Ali Univ., Tehran, Iran

DOI: https://doi.org/10.37863/umzh.v73i11.1069

Ключові слова: Vanishing element, finite simple groups, Vanishing prime graph

Анотація

УДК 512.5

Нехай $G$ — скiнченна група. Елемент $g \in G$ є зникаючим елементом, якщо iснує незвiдний комплексний характер $\chi \in G$ такий, що $\chi (g) = 0$. Гасемабадi, Iранманеш та Мавадатпур (2015) запропонували гiпотезу: якщо $G$ — скiнченна група, а $M$ — скiнченна неабелева проста група, для яких $\mathrm{V}\mathrm{o} (G) = \mathrm{V}\mathrm{o} (M)$ та $| G| = | M|$ , тодi $G \cong M $.
Ми доводимо цю гiпотезу для $M = ^2 D_{r+1}(2)$, де $r = 2n - 1 \geq 3$, якщо або $2^r + 1$, або $2^{r+1}+1$ є простим числом та для $M = ^2 D_{r}(3)$, де $r = 2^n + 1 \geq 5$, якщо або $(3^{r-1}+1)/2$ , або $(3^{r}+1)/4$ є простим.

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