In this paper, we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. These groups have recently been investigated in terms of their abstract structure, in a similar way to the O'Nan–Scott Theorem for primitive groups. Our goal here is to explore aspects of such groups which may be useful in place of precise structural information. We give bounds on the order, base size, minimal degree, fixed point ratio, and chief length of an arbitrary finite semiprimitive group in terms of its degree. To establish these bounds, we study the structure of a finite semiprimitive group that induces the alternating or symmetric group on the set of orbits of an intransitive minimal normal subgroup.

中文翻译：

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有限半原始置换群的界限：阶数、基数和最小度数

在本文中，我们研究有限半原始置换群，即每个正规子群都是传递或半正则的群。这些群最近已经根据它们的抽象结构进行了研究，类似于原始群的 O'Nan-Scott 定理。我们的目标是探索这些组的各个方面，这些方面可能有助于代替精确的结构信息。我们根据度数给出任意有限半原始群的阶数、基数、最小度数、不动点比和主长度的界限。为了建立这些界限，我们研究了一个有限半原始群的结构，该群在不及物最小正规子群的轨道集上引发了交替或对称群。