The distinguishing number of quasiprimitive and semiprimitive groups

Alice Devillers; Luke Morgan; Scott Harper

doi:10.1007/s00013-019-01324-7

The distinguishing number of quasiprimitive and semiprimitive groups

Alice Devillers, Luke Morgan^*, Scott Harper

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

The distinguishing number of G⩽ Sym (Ω) is the smallest size of a partition of Ω such that only the identity of G fixes all the parts of the partition. Extending earlier results of Cameron, Neumann, Saxl, and Seress on the distinguishing number of finite primitive groups, we show that all imprimitive quasiprimitive groups have distinguishing number two, and all non-quasiprimitive semiprimitive groups have distinguishing number two, except for GL (2 , 3) acting on the eight non-zero vectors of F32, which has distinguishing number three.

Original language	English
Pages (from-to)	127-139
Number of pages	13
Journal	Archiv der Mathematik
Volume	113
Issue number	2
Early online date	30 Apr 2019
DOIs	https://doi.org/10.1007/s00013-019-01324-7 https://doi.org/10.1007/s00013-019-01324-7
Publication status	Published - 1 Aug 2019

Keywords

Distinguishing number
Permutation group
Primitive groups
Symmetric graphs

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AB - The distinguishing number of G⩽ Sym (Ω) is the smallest size of a partition of Ω such that only the identity of G fixes all the parts of the partition. Extending earlier results of Cameron, Neumann, Saxl, and Seress on the distinguishing number of finite primitive groups, we show that all imprimitive quasiprimitive groups have distinguishing number two, and all non-quasiprimitive semiprimitive groups have distinguishing number two, except for GL (2 , 3) acting on the eight non-zero vectors of F32, which has distinguishing number three.

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KW - Symmetric graphs

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JO - Archiv der Mathematik

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The distinguishing number of quasiprimitive and semiprimitive groups

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Keywords

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