Distinguishing Primitive Permutation Groups

Chris Godsil

Distinguishing Primitive Permutation Groups

Combinatorics 2009-11-04 v2 Group Theory

Authors: Chris Godsil

Abstract

Let $G$ be a permutation group acting on a set $V$ . A partition $\pi$ of $V$ is distinguishing if the only element of $G$ that fixes each cell of $\pi$ is the identity. The distinguishing number of $G$ is the minimum number of cells in a distinguishing partition. We prove that if $G$ is a primitive permutation group and $|V|\ge336$ , its distinguishing number is two.

Keywords

permutation groups

Cite

@article{arxiv.0806.2078,
  title  = {Distinguishing Primitive Permutation Groups},
  author = {Chris Godsil},
  journal= {arXiv preprint arXiv:0806.2078},
  year   = {2009}
}

Comments

A much stronger result was obtained earlier by Seress. His result is now cited. Since my methods might be of some interest, I have chosen to replace rather than withdraw the paper. It will not be submitted for publication

Distinguishing Primitive Permutation Groups

Abstract

Keywords

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