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We revisit, clarify, and generalise classical results of Dickson and (muchlater) Wagner on minimal Sym(n)- and Alt(n)-modules. We present a new, naturalnotion of 'modules with an additive dimension' covering at once the classical,finitary case as well as modules definable in an o-minimal or finite Morleyrank setting; in this context, we fully identify the faithful Sym(n)- andAlt(n)-modules of least dimension.

Sym(n)- and Alt(n)-modules with an additive dimension