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A criterion for a finite permutation group to be transitive
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Julian Brough
Published/Copyright:
October 24, 2015
Abstract
Let G be a finite permutation group on a finite set Ω. We say that G is quasi-transitive if every 2-point stabiliser has the same order. This notion was introduced by Alan Camina. In particular, Camina established conditions for a quasi-transitive group to be transitive. The aim of this note is to validate Camina's conjecture: A quasi-transitive group G on a finite set Ω is transitive on Ω.
The author would like to express his thanks to the referee for helpful suggestions, and improvements to the presentation of the proof.
Received: 2015-7-20
Revised: 2015-8-18
Published Online: 2015-10-24
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups
- Residual properties of graph products of groups
- On hereditarily just infinite profinite groups obtained via iterated wreath products
- Weak commutativity between two isomorphic polycyclic groups
- Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions
- Finite groups in which pronormality and 𝔉-pronormality coincide
- Towards Thompson's conjecture for alternating and symmetric groups
- Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
- A criterion for a finite permutation group to be transitive
- Inverse Glauberman–Isaacs correspondence and subnormal subgroups
