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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.
|Number of pages||13|
|Journal||Archiv der Mathematik|
|Early online date||30 Apr 2019|
|Publication status||Published - 1 Aug 2019|
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- 1 Finished
Structure theory for permutation groups and local graph theory conjectures
1/01/16 → 31/01/19