On Cameron’s question about primitive permutation groups with stabilizer of two points that is normal in the stabilizer of one of them

Konygin, A. V.

doi:10.1134/s0081543814050125

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…This question was also proposed by Fomin in the Kourovka Notebook [14,Question 9.69]. Remarkable evidence towards the veracity of the question of Cameron and Fomin is given by Konygin [8,9,10,11], however to the best of our knowledge this question is still open. To some extent, Conjecture 1.2 can be seen as a generalization of the question of Cameron and Fomin, allowing G αβ G α , but relaxing the conclusion when G αβ G α .…”

Section: Theorem 11 (Sims Conjecture)mentioning

confidence: 67%

A generalization of Sims conjecture for finite primitive groups and two point stabilizers in primitive groups

Spiga¹

2021

Preprint

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In this paper we propose a refinement of Sims conjecture concerning the cardinality of the point stabilizers in finite primitive groups and we make some progress towards this refinement.In this process, when dealing with primitive groups of diagonal type, we construct a finite primitive group G on Ω and two distinct points α, β ∈ Ω with G αβ Gα and G αβ = 1, where Gα is the stabilizer of α in G and G αβ is the stabilizer of α and β in G. In particular, this example gives an answer to a question raised independently by Peter Cameron in [3] and by Alexander Fomin in the Kourovka Notebook [14, Question 9.69].

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Section: Theorem 11 (Sims Conjecture)mentioning

confidence: 67%

A generalization of Sims conjecture for finite primitive groups and two point stabilizers in primitive groups

Spiga¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…This question was also proposed by Fomin in the Kourovka Notebook [16, Question 9.69]. 1 Remarkable evidence for a positive answer to the question is given by Konygin [10][11][12][13]; however, to the best of our knowledge, this question is still open. To some extent, Conjecture 1.2 can be seen as a generalization of the Cameron-Fomin question, allowing G ˛ˇ6 E G ˛, but relaxing the conclusion for G ˛ˇE G ˛.…”

Section: Theorem 11 (Sims Conjecture)mentioning

confidence: 82%

A generalization of Sims’ conjecture for finite primitive groups and two point stabilizers in primitive groups

Spiga

2021

Journal of Group Theory

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In this paper, we propose a refinement of Sims’ conjecture concerning the cardinality of the point stabilizers in finite primitive groups, and we make some progress towards this refinement. In this process, when dealing with primitive groups of diagonal type, we construct a finite primitive group 𝐺 on Ω and two distinct points α , β ∈ Ω \alpha,\beta\in\Omega with G α ⁢ β ⊴ G α G_{\alpha\beta}\unlhd G_{\alpha} and G α ⁢ β ≠ 1 G_{\alpha\beta}\neq 1 , where G α G_{\alpha} is the stabilizer of 𝛼 in 𝐺 and G α ⁢ β G_{\alpha\beta} is the stabilizer of 𝛼 and 𝛽 in 𝐺. In particular, this example gives an answer to a question raised independently by Cameron and by Fomin in the Kourovka Notebook.

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On Cameron’s question about primitive permutation groups with stabilizer of two points that is normal in the stabilizer of one of them

Cited by 2 publications

References 13 publications

A generalization of Sims conjecture for finite primitive groups and two point stabilizers in primitive groups

A generalization of Sims conjecture for finite primitive groups and two point stabilizers in primitive groups

A generalization of Sims’ conjecture for finite primitive groups and two point stabilizers in primitive groups

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