## Abstract

We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer G_{α}is nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement.

Original language | English |
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Pages (from-to) | 1041-1048 |

Number of pages | 8 |

Journal | Siberian Mathematical Journal |

Volume | 63 |

Issue number | 6 |

DOIs | |

Publication status | Published - Nov 2022 |

## Keywords

- 2-homogeneous group
- 2-transitive group
- 3/2-transitive group
- Frobenius complement
- minimal generating set
- primitive permutation group

## OECD FOS+WOS

- 1.01 MATHEMATICS