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2015•Journal of Group TheoryRequires access

A criterion for a finite permutation group to be transitive

Julian Brough

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Transitive relation, Mathematics, Permutation group, Primitive permutation group, Combinatorics, Permutation (music), Group (periodic table), Conjecture

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