2022/02/21 by Noah Caplinger, Caplinger, Noah, Nick Salter +1 · 1 citation
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Graph theory and applications #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2202.10216
openalex publication_date 2022/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.