On decompositions of matrices into products of commutators of involutions

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.

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Bibliographische Detailangaben
Veröffentlicht in:	The Electronic journal of linear algebra 2022-02, p.123-130
Hauptverfasser:	Nam Son, Tran, Huu Dung, Truong, Thi Thai Ha, Nguyen, Hoang Bien, Mai
Format:	Artikel
Sprache:	eng
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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.
ISSN:	1081-3810 1081-3810
DOI:	10.13001/ela.2022.6797