On the base size and rank of a primitive permutation group (Q1355663)
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scientific article; zbMATH DE number 1014046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the base size and rank of a primitive permutation group |
scientific article; zbMATH DE number 1014046 |
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On the base size and rank of a primitive permutation group (English)
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22 October 1997
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Let \(G\) be a finite primitive permutation group of rank \(r\) acting on a set \(\Omega\) of size \(n\). Further, let \(\chi\) be a nontrivial irreducible constituent of the permutation character of \(G\) on \(\Omega\), occurring with multiplicity \(m\), and let \(b\) be the size of any irredundant base in \(\Omega\) for \(G\). It is proved that \(b\leq(n-1)/(r-1)\) and \(b\leq\chi(1)/m\).
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finite primitive permutation groups
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rank
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base sizes
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permutation characters
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