| Characterization of $L_2(16)$ by $\tau_e(L_2(16))$ |
| Received:September 14, 2010 Revised:April 18, 2011 |
| Key Words:
element orders recognizable number of elements same order Thompson problem.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11171364). |
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| Abstract: |
| Let $G$ be a group and $\pi_e(G)$ the set of element orders of $G$. Let $k\in \pi_e(G)$ and $m_k$ be the number of elements of order $k$ in $G$. Let $\tau_e(G)=\{m_k |k\in \pi_e(G)\}$. In this paper, we prove that $L_2(16)$ is recognizable by $\tau_e(L_2(16))$. In other words, we prove that if $G$ is a group such that $\tau_e(G)=\tau_e(L_2(16))=\{1, 255, 272, 544, 1088, 1920\}$, then $G$ is isomorphic to $L_2(16)$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.02.013 |
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