论文标题
用于原始$ \ frac {3} {2} $的生成集的最小尺寸
The minimal size of a generating set for primitive $\frac{3}{2}$-transitive groups
论文作者
论文摘要
我们将$ d（g）$称为有限组$ g $的生成集的最小基数，并说如果$ d $ d $如果$ d（g）\ leq d $会产生$ d $。如果点稳定器$g_α$是非平底的，并且其轨道与$ \ {α\} $不同，则及时置换式组$ g $称为$ \ frac {3} {2} $ - 及时呈频率。我们证明，每个原始$ \ frac {3} {2} $的$ d（g）\ leq4 $ - transitive置换式$ g $，此外，$ g $是$ 2 $ $ 2 $生成的，除了我们完全描述的非常特殊的可解决的仿期组。特别是，所有有限的$ 2 $变态和$ 2 $ - 均匀的群体都是$ 2 $生成的。我们还表明，每个有限型组的循环均为$ 2 $，因此每个Frobenius的补充也是如此。
We refer to $d(G)$ as the minimal cardinality of a generating set of a finite group $G$, and say that $G$ is $d$-generated if $d(G)\leq d$. A transitive permutation group $G$ is called $\frac{3}{2}$-transitive if a point stabilizer $G_α$ is nontrivial and its orbits distinct from $\{α\}$ are of the same size. We prove that $d(G)\leq4$ for every primitive $\frac{3}{2}$-transitive permutation group $G$, moreover, $G$ is $2$-generated except for the very particular solvable affine groups that we completely describe. 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.
