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Remarks on N=1 supersymmetric extension of the Euler top

A natural N=1 supersymmetric extension of the Euler top, which introduces exactly one fermionic counterpart for each bosonic degree of freedom, is considered. The equations of motion, their symmetries and integrals of motion are given. It is demonstrated that, although in general the system lacks the integrability property, it admits an interesting integrable reduction, for which all fermions are proportional to one and the same Grassmann-odd number - a value of the conserved supercharge. A generalisation involving an arbitrary three-dimensional real Lie algebra is proposed.