The distinguishing number of quasiprimitive and semiprimitive groups

Alice Devillers, Luke Morgan*, Scott Harper

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
164 Downloads (Pure)

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 languageEnglish
Pages (from-to)127-139
Number of pages13
JournalArchiv der Mathematik
Volume113
Issue number2
Early online date30 Apr 2019
DOIs
Publication statusPublished - 1 Aug 2019

Keywords

  • Distinguishing number
  • Permutation group
  • Primitive groups
  • Symmetric graphs

Fingerprint Dive into the research topics of 'The distinguishing number of quasiprimitive and semiprimitive groups'. Together they form a unique fingerprint.

Cite this