Abstract
A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the algebraic structure. In this paper we introduce a more general perspective on total symmetry and formulate a notion of “irreducibility” for totally symmetric sets in the general linear group. We classify irreducible totally symmetric sets, as well as those of maximal cardinality.
Citation
Noah Caplinger. Nick Salter. "Totally Symmetric Sets in the General Linear Group." Michigan Math. J. Advance Publication 1 - 56, 2023. https://doi.org/10.1307/mmj/20226262
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