# Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size, and Minimal Degree

@article{Morgan2018BoundsFF, title={Bounds for Finite Semiprimitive Permutation Groups: Order, Base Size, and Minimal Degree}, author={Luke Morgan and Cheryl E. Praeger and Kyle Rosa}, journal={arXiv: Group Theory}, year={2018} }

In this paper we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. We give bounds on the order, base size, minimal degree, fixity, and chief length of an arbitrary finite semiprimitive group in terms of its degree. To establish these bounds, we classify finite semiprimitive groups that induce the alternating or symmetric group on the set of orbits of an intransitive normal subgroup.

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