Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree. Issue 4 (5th November 2020)

• Record Type: Journal Article
• Authors: Morgan, Luke; Praeger, Cheryl E.; Rosa, Kyle
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 63:Issue 4(2020)
• Page Start: 1071
• Page End: 1091
• Publication Date: 2020-11-05
• Subjects: Permutation groups, -- base size, -- minimal degree; 20B05, -- 20B15; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091520000346
• Languages: English
• ISSNs: 0013-0915

Abstract

Abstract: 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.