I. INTRODUCTION Over the past three decades, the orbital dynamics of two-dimensional (2D) electrons coupled to a uniform perpendicular magnetic field has been a subject of special interest in condensed matter physics. Great attention has been paid to investigate the well-known Hofstadter butterfly-like diagram, a remarkable intricate, detailed, and self-similar feature for the subband spectrum of single-particle eigenenergies, in different 2D structures such as square [1], triangular [2], honeycomb [3], and kagom´ e lattices [4], lateral superlattices [5], superstructures with flat bands [6], quasiperiodic tilings [7], fractal networks [8], and rhombus tilings [9]. This magnetic-field-induced frustration in 2D structures, caused by the competition between the periodic potential imposed by the lattice structure and the length scale provided by the magnetic field, is the headstream of rich and novel physical phenomena in these 2D systems. Among them the orbital magnetization is a very interesting one and needs to be paid special attention due to its intrinsic relationship with the unique topological structure brought about by the interplay between the special lattice geometry and magnetic subbands. Unfortunately, to date, there are very scarce studies [10, 11] in literature that devote to enlightening this revealing relationship. Motivated by this observation, in this paper, we study the orbital magnetization proper- ties of the electron gas on a two-dimensional kagom´ e lattice under a perpendicular magnetic field. Since our attention is solely on the orbital character in magnetization brought about by the interplay between the kagom´ e lattice structure and the magnetic field, thus unlike most of previous work, the kagom´ e lattice considered in this paper is spin nonmagnetic in itself, namely, no spin structure is exposed in the absence of the external magnetic field. The nonmagnetic kagom´ e lattice structure has been either fabricated by modern patterning techniques [12, 13] or observed in reconstructed semiconductor surfaces [14]. In the former case, remarkably, the electron filling factor (namely, the Fermi energy) can be readily con- trolled by applying a gate voltage [15]. Our lattice model is free from the constraint imposed on the k · p approximation used in the extensively studied GaAs two-dimensional electron gas (2DEG), in which the k · p Hamiltonian is only valid around the Γ point in the Brillouin zone (BZ). In contrast, our lattice model allows for any electron filling, which result in var- ious Fermi-surface topologies in the magnetic BZ, which in turn, as will be shown below, produces profound effects on the orbital magnetization properties and the related transport 2