On the \(\varphi\)-structure on the projective group \(L_2(q)\) (Q1280635)
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scientific article; zbMATH DE number 1262503
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(\varphi\)-structure on the projective group \(L_2(q)\) |
scientific article; zbMATH DE number 1262503 |
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On the \(\varphi\)-structure on the projective group \(L_2(q)\) (English)
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17 July 2000
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If \(f\) is a non-identical automorphism of the projective group \(G=L_2(q)\), then there exist \(a,b\) in \(G\) such that \(df(c)=cd\), where \(c=af(a)^{-1}\neq 1\) and \(d=b^{-1}f(b)\). As a consequence, the group \(G\) is not isomorphic to the automorphism group of any finite left distributive quasigroup (i.e., a quasigroup satisfying \(x.yz=xy.xz\)).
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projective groups
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automorphism groups
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finite left distributive quasigroups
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