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

Abstract In this paper, we propose a refinement of Sims’ conjecture concerning the cardinality point stabilizers in finite primitive groups, and make some progress towards refinement. process, when dealing with groups diagonal type, construct group ???? on ? two distinct points ?,??? \alpha,\beta\in\Omega xmlns:m="http://www.w3.org/1998/Math/MathML">G????G? G_{\alpha\beta}\unlhd G_{\alpha} xmlns:m="http://www.w3.org/1998/Math/MathML">G????1 G_{\alpha\beta}\neq 1 , where xmlns:m="http://www.w3.org/1998/Math/MathML">G? is stabilizer ???? xmlns:m="http://www.w3.org/1998/Math/MathML">G??? G_{\alpha\beta} ???? ????. particular, example gives an answer to question raised independently by Cameron Fomin Kourovka Notebook.