A 3-local characterization of \(M_{12}\) and \(\text{SL}_3(3)\). (Q1018042)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A 3-local characterization of \(M_{12}\) and \(\text{SL}_3(3)\). |
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A 3-local characterization of \(M_{12}\) and \(\text{SL}_3(3)\). (English)
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13 May 2009
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The authors prove the following theorem: Let \(G\) be a finite group, \(A,B\leq G\), \(A\neq B\) and \(S\in\text{Syl}_3(G)\). If \(G=\langle A,B\rangle\), \(A\cong B\cong\text{AGL}_2(3)\) and \(N_G(Z(S))\leq A\) then \(G\cong\text{SL}_3(3)\) or \(G\cong M_{12}\). They also present a graph theoretic analogue of this theorem.
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finite groups
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self-centralizing subgroups
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local characteristic \(p\)
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\(p\)-local subgroups
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sporadic groups
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graphs
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