Recognition of alternating groups of degrees \(r+1\) and \(r+2\) for prime \(r\) and the group of degree \(16\) by the set of their element orders (Q2746922)
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scientific article; zbMATH DE number 1656860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Recognition of alternating groups of degrees \(r+1\) and \(r+2\) for prime \(r\) and the group of degree \(16\) by the set of their element orders |
scientific article; zbMATH DE number 1656860 |
Statements
11 October 2001
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element orders
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recognizable groups
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Gruenberg-Kegel graphs
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alternating groups
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Recognition of alternating groups of degrees \(r+1\) and \(r+2\) for prime \(r\) and the group of degree \(16\) by the set of their element orders (English)
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\textit{A.~S.~Kondrat'ev} and \textit{V.~D.~Mazurov} [Sib. Mat. Zh. 41, No. 2, 359-369 (2000; Zbl 0956.20007)] proved that an alternating group of prime degree \(r\) is recognizable. By using the same arguments, the author proves that alternating groups of degree \(r+1\) and \(r+2\) are also recognizable. The author also proves that the alternating group of degree 16 is recognizable. This is the first example of a recognizable group with connected Gruenberg-Kegel graph.
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