On quadrilaterals in the suborbital graphs of the normalizer

n this paper‎, ‎we investigate suborbital graphs formed by $N\big(\Gamma_۰(N)\big)$-invariant equivalence relation induced on $\hat{\mathbb{Q}}$‎. ‎Conditions for being an edge are obtained as a main tool‎, ‎then necessary and sufficient conditions for the suborbital graphs to contain a circuit are investigated‎.

کلیدواژه ها:

‎Normalizer‎ ، ‎Imprimitive action‎ ، ‎Suborbital graphs