Projects per year
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'NanScott 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.
Original language  English 

Pages (fromto)  10711091 
Number of pages  21 
Journal  Proceedings of the Edinburgh Mathematical Society 
Volume  63 
Issue number  4 
DOIs  
Publication status  Published  4 Nov 2020 
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Dive into the research topics of 'Bounds for finite semiprimitive permutation groups: Order, base size, and minimal degree'. Together they form a unique fingerprint.Projects
 2 Finished

Structure theory for permutation groups and local graph theory conjectures
ARC Australian Research Council
1/01/16 → 31/01/19
Project: Research

Permutation groups: factorisations, structure and applications
ARC Australian Research Council
1/01/16 → 2/02/19
Project: Research