Primitivity of permutation groups, coherent algebras and matrices

Gareth A. Jones; Mikhail Klin; Yossi Moshe

doi:10.1006/jcta.2001.3245

Primitivity of permutation groups, coherent algebras and matrices

Gareth A. Jones, Mikhail Klin, Yossi Moshe

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras.

Original language	English
Pages (from-to)	210-217
Number of pages	8
Journal	Journal of Combinatorial Theory - Series A
Volume	98
Issue number	1
DOIs	https://doi.org/10.1006/jcta.2001.3245
State	Published - 1 Jan 2002

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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abstract = "A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras.",

author = "Jones, {Gareth A.} and Mikhail Klin and Yossi Moshe",

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AU - Moshe, Yossi

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N2 - A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras.

AB - A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras.

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Primitivity of permutation groups, coherent algebras and matrices

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