Submission date: 22 November 2021

Abstract:

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

Mathematics Subject Classification: Primary 20C30, Secondary 03C60, 20F11

Keywords and phrases:

Full text arXiv 2111.11498: pdf, ps.