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arXiv · 2202.10216

Totally symmetric sets in the general linear group

Noah Caplinger·Nick Salter
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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.

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Noah Caplinger, Nick Salter. 2022-02-21. Totally symmetric sets in the general linear group. https://arxiv.org/abs/2202.10216

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