On decompositions of matrices into products of commutators of involutions
Tran Nam Son, Truong Huu Dung, Nguyen Thi Thai Ha, Mai Hoang Bien
Abstract
Let $F$ be a field and let $n$ be a natural number greater than $1$. The aim of this paper is to prove that if $F$ contains at least three elements, then every matrix in the special linear group $\mathrm{SL}_n(F)$ is a product of at most two commutators of involutions.
Topics & Concepts
MathematicsProduct (mathematics)Pure mathematicsMatrix (chemical analysis)Field (mathematics)General linear groupCombinatoricsAlgebra over a fieldSymmetric groupGeometryMaterials scienceComposite materialFinite Group Theory ResearchAdvanced Topics in Algebragraph theory and CDMA systems