Elliptic elements of Γ∧0,n(N), act on DOUBLE-STRUCK CAPITAL Q∧(N) and suborbital graphs of Γ∧0,n(N) on the group DOUBLE-STRUCK CAPITAL Q∧(N)

Abstract

First, It is proved that there are no second and third order elliptic elements under conditions of n | N and n inverted iota 24 in Gamma(0,n)(N). Gamma(0,n)(N) is a subset of group Gamma(0)(N) and n, N is an element of Z(+). Second we define an invariant equivalence relation on (Q) over cap (N) of Gamma(0)(N), and obtain some properties. Third we again define an invariant equivalence relation on (Q) over cap (N) of group (Gamma) over cap (0,n)(N). Then we investigate its suborbital graphs. Finally we research some properties of graph F-u,N(*) for n | N and n inverted iota 24, n, N is an element of Z(+).