## Abstract

In the first paper in this series we estimated the probability that a random permutation π ∈ S
_{n} has a fixed set of a given size. In this paper, we elaborate on the same method to estimate the probability that p has m disjoint fixed sets of prescribed sizes k
_{1},..,k
_{m}, where k
_{1}+···+k
_{m} = n. We deduce an estimate for the proportion of permutations contained in a transitive subgroup other than S
_{n} or A
_{n}. This theorem consists of two parts: an estimate for the proportion of permutations contained in an imprimitive transitive subgroup, and an estimate for the proportion of permutations contained in a primitive subgroup other than S
_{n} or A
_{n}.

Original language | English (US) |
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Pages (from-to) | 1-36 |

Number of pages | 36 |

Journal | Discrete Anal. |

Volume | 12 |

Issue number | 2016 |

DOIs | |

State | Published - 2016 |

## Keywords

- Primitive groups
- Transitive groups
- Łuczak-Pyber theorem

## ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics