Recent zbMATH articles in MSC 20H https://zbmath.org/atom/cc/20H 2022-07-25T18:03:43.254055Z Werkzeug On decompositions of matrices into products of commutators of involutions https://zbmath.org/1487.15015 2022-07-25T18:03:43.254055Z "Son, Tran Nam" https://zbmath.org/authors/?q=ai:son.tran-nam "Dung, Truong Huu" https://zbmath.org/authors/?q=ai:dung.truong-huu "Ha, Nguyen Thi Thai" https://zbmath.org/authors/?q=ai:ha.nguyen-thi-thai "Bien, Mai Hoang" https://zbmath.org/authors/?q=ai:mai-hoang-bien. Let $$\mathbb{F}$$ be a field with at least three elements. Denote by $$\mathrm{SL}_n(\mathbb{F})$$ the set of $$n \times n$$ matrices with entries in $$\mathbb{F}$$ and with determinant 1. A matrix $$A$$ is an involution if $$A^2 = I_n$$, where $$I_n$$ is the $$n \times n$$ identity matrix. A commutator of two involutions is of the form $$BCB^{-1}C^{-1}$$, where $$B$$ and $$C$$ are involutions. The main theorem of the paper is the following: If $$n$$ is a natural greater than 1, then every matrix in $$\mathrm{SL}_n(\mathbb{F})$$ is a product of at most two commutators of involutions. Reviewer: Julio Benítez Lopez (Valencia)