Suborbital Graphs for a Special Subgroup of the SL(3;Z)

Abstract

In this paper, we examine some properties of suborbital graphs for the group SL(3;Z). We first, introduce an invariant equivalence relation by using the congruence subgroup SL(3;Z) instead of Gamma0(n) and obtain some results for the newly constructed subgraphs Fu;n whose vertices form the block [1]. We obtain edge and circuit conditions and some relations between lengths of circuits in Fu;n and elliptic elements of Gamma0(n).