An involution in a group \(G\) is an element \(x\) in \(G\) such that \(x^ 2 = 1\). Every element with determinant \(\pm 1\) in the general linear group is a product of four or fewer involutions. Every element in the symmetric group \(S_ n\) is a product of two involutions. The author discusses products of involutions in various groups, especially in groups of matrices. The considerations include suggestions for further research for groups of matrices with entries in rings.
For the entire collection see [Zbl 0777.00059].