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We complete a classification of the groups of endotrivial modules for the modular group algebras of symmetric groups and alternating groups. We show that for n ≥ p 2 the torsion subgroup of the group of endotrivial modules for the symmetric groups is generated by the sign representation. The torsion subgroup is trivial for the alternating groups.doi:10.1017/s0013091508000618 fatcat:f3ayr3lbujd75gttszk63kyqli