NSE characterization of projective special linear group \(L_5(2)\). (Q481032)
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scientific article; zbMATH DE number 6379720
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | NSE characterization of projective special linear group \(L_5(2)\). |
scientific article; zbMATH DE number 6379720 |
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NSE characterization of projective special linear group \(L_5(2)\). (English)
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12 December 2014
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Summary: 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 \(\mathrm{nse}(G)=\{s_k\mid k\in\omega(G)\}\). In Khatami et al. and Liu, \(L_3(2)\) and \(L_3(4)\) are uniquely determined by \(\mathrm{nse}(G)\). In this paper, we prove that if \(G\) is a group such that \(\mathrm{nse}(G)=\mathrm{nse}(L_5(2))\), then \(G\cong L_5(2)\).
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projective special linear groups
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Thompson problem
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characterizable groups
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sets of numbers of elements of equal orders
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sets of element orders
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nse
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finite simple groups
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