Abelian point stabilizers in transitive permutation groups (Q2782618)
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scientific article; zbMATH DE number 1725311
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Abelian point stabilizers in transitive permutation groups |
scientific article; zbMATH DE number 1725311 |
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Abelian point stabilizers in transitive permutation groups (English)
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8 April 2002
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point-stabilizers
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transitive permutation groups
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\textit{A. Lucchini} [Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 9, No. 4, 241-243 (1998; Zbl 0940.20006)] proved that if a point-stabilizer \(A\) in a transitive permutation group of degree \(m>1\) is cyclic, then \(|A|<m\). The author proves here a stronger result: if a point-stabilizer \(A\) in a transitive permutation group of degree \(m>1\) is Abelian, then \(\exp(A)<m\).
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