\(p\)-groups in the Betti-Mathieu group (Q1908191)
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scientific article; zbMATH DE number 847496
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(p\)-groups in the Betti-Mathieu group |
scientific article; zbMATH DE number 847496 |
Statements
\(p\)-groups in the Betti-Mathieu group (English)
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17 July 1996
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The author looks at the Betti-Mathieu group which is formed from a certain set of permutation polynomials under composition. A Sylow \(p\)-subgroup of this group is constructed via characterization of a certain type of polynomial by use of the trace function and a normal basis over a finite field. Thereby the author is able to determine a complete lattice of normal subgroups of this Sylow \(p\)-subgroup. Also, an explicit polynomial representation of the normal subgroups is given.
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polynomial representation of normal subgroups
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Betti-Mathieu group
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permutation polynomials
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Sylow \(p\)-subgroup
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