Rendiconti del Seminario Matematico della Università di Padova


Full-Text PDF (103 KB) | Metadata | Table of Contents | RSMUP summary
Volume 132, 2014, pp. 123–132
DOI: 10.4171/RSMUP/132-9

NSE characterization of projective special linear group $L_5(2)$

Shitian Liu[1]

(1) Sichuan University of Science and Engineering, China

Let $ G$ be a group and $ {\omega} (G)$ be the set of element orders of $ G$. Let $ k\in {\omega} (G)$ and $ s_ {k}$ be the number of elements of order $ k$ in $ G$. Let nse$ (G)=\big \{ s_{k}\,\big \vert \;k\in {\omega} (G) \big \}$. In Khatami et al. and Liu, $ L_ {3}(2)$ and $ L_ {3}(4)$ are uniquely determined by nse$ (G)$. In this paper, we prove that if $ G$ is a group such that nse$ (G)= nse( L_ {5}(2)$), then $ G\cong L_ {5}(2)$.

Keywords: Element order, projective special linear group, Thompson's problem, number of elements of the same order

Liu Shitian: NSE characterization of projective special linear group $L_5(2)$. Rend. Sem. Mat. Univ. Padova 132 (2014), 123-132. doi: 10.4171/RSMUP/132-9