On the Action of \Gamma ^0(N) on \hat{\mathbb{Q}}


Abstract


In this paper we examine \Gamma ^0(N)-orbits on \hat{\mathbb{Q}}and the suborbital graphs for \Gamma ^0(N). Each such suborbitalgraph is a disjoint union of subgraphs whose vertices form a blockof imprimitivity for \Gamma ^0(N). Moreover, these subgraphs areshown to be vertex \Gamma ^0(N)-transitive and edge \Gamma^0(N)-transitive. Finally, necessary and sufficient conditions forbeing self-paired edge are provided.

DOI Code: 10.1285/i15900932v30n2p141

Keywords: Congruence groups; Transitive and Imprimitive action; Suborbital graphs

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