Submission date: 8 May 2024

Abstract:

Working in the general context of “modules with an additive dimension”, we complete the determination of the minimal dimension of a faithful Alt(n)-module and classify those modules in three of the exceptional cases: 2-dimensional Alt(5)-modules in characteristic 2, 3-dimensional Alt(5)-modules in characteristic 5, and 3-dimensional Alt(6)-modules in characteristic 3. We also highlight the remaining work needed to complete the classification of the faithful Alt(n)-modules of minimal dimension for all n; these open problems seem well suited as projects for advanced undergraduate or master's students.

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

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Full text arXiv 2405.05230: pdf, ps).