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

  • S. Askary Imam-Ali Univ., Tehran, Iran
Keywords: Vanishing element, finite simple groups, Vanishing prime graph


UDC 512.5

Характеризацiя деяких скiнченних простих груп множиною порядкiв зникаючих елементiв та порядку

Let $G$ be a finite group. We say that an element $g$ of $G$ is a vanishing element if there exists an irreducible complex character $X$ of $G$ such that $X(g) = 0$. Ghasemabadi, Iranmanesh, Mavadatpour (2015), present the following conjecture: Let $G$ be a finite group and $M$ a finite nonabelian simple group such that $Vo(G)=Vo(M)$ and $|G|=|M|$. Then $G \cong M $. We answer in affirmative this conjecture for $M = ^2 D_{r+1}(2)$, where $r = 2^n - 1 \geq 3$ and either $2^r+1$ or $2^{r+1}+1$ is a prime number and $M = ^2 D_{r}(3)$, where $r = 2^n + 1 \geq 5$ and either $(3^{r-1}+1)/2$ or $(3^{r}+1)/4$ is prime.


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How to Cite
Askary, S. “Characterization of Some Finite Simple Groups by the Set of Orders of Vanishing Elements and Order”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 11, Nov. 2021, pp. 1443 -50, doi:10.37863/umzh.v73i11.1069.
Research articles