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The stability against low‐frequency, electrostatic, flute‐like oscillations of a tenuous, hot, plane layer of charged particles embedded in a uniform and constant magnetic field is considered. It is shown that finite Larmor radius effects do not modify essentially the diocotron modes. It is also shown that a layer of particles whose guiding centers are located on a thin (with respect to the thickness of the layer) sheet around the midplane of the layer, is unstable: more precisely it has, for long (with respect to the thickness of the layer) waves, the same dispersion relation which holds for the diocotron modes. This strongly supports the conclusion that the diocotron instability of a charged, tenuous, plane layer is essentially independent from its kinetic structure.