NSE CHARACTERIZATION OF THE SIMPLE GROUP $L_2(3^n)$

Hosein Parvizi Mosaed, Ali Iranmanesh, Abolfazl Tehranian

Abstract: Let $G$ be a group and $\pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $\operatorname{nse}(G)$ be the set of the numbers of elements of $G$ of the same order. We prove that the simple group $L_2(3^n)$ is uniquely determined by $\operatorname{nse}(L_2(3^n))$, where $|\pi(L_2(3^n))|=4$.

Keywords: Element order; set of the numbers of elements of the same order; projective special linear group

Classification (MSC2000): 20D60; 20D06

Full text of the article: (for faster download, first choose a mirror)

• Compressed DVI file (28 kilobytes)
• Compressed PostScript file (428 kilobytes)
• PDF file (156 kilobytes)