The general position number \(\mathrm{gp}(G)\) of a connected graph G is the cardinality of a largest set S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets are refereed to as gp-sets of G. The general position number of cylinders \(P_r\,\square \,C_s\) is deduced. It is proved that \(\mathrm{gp}(C_r\,\square \,C_s)\in \{6,7\}\) whenever \(r\ge s \ge 3\), \(s\ne 4\), and \(r\ge 6\). A probabilistic lower bound on the general position number of Cartesian graph powers is achieved. Along the way a formula for the number of gp-sets in \(P_r\,\square \,P_s\), where \(r,s\ge 2\), is also determined.

连通图G的总位置数\（\ mathrm {gp}（G）\）是最大顶点集S的基数，因此从S出发，没有三个不同的顶点位于同一个测地线上。这样的集合称为G的gp集。推导出圆柱体的一般位置数\（P_r \，\ square \，C_s \）。证明\（\ mathrm {gp}（C_r \，\ square \，C_s）\ in \ {6,7 \} \）每当\（r \ ge s \ ge 3 \），\（s \ ne 4 \）和\（r \ ge 6 \）。实现了笛卡尔图幂的一般位置数的概率下界。一路走来的gp集数量的公式\（P_r \，\ square \，P_s \），其中\（r，s \ ge 2 \）也是确定的。