Characterization of groups of involutions and pseudo-involutions and construction of groups of involutions

An n × n matrix A over a field F is an involution if A² = I_n. If the characteristic of F = p then A is a pseudo- n involution if A + A^-1 = 2I_n. If the characteristic of F = 2 then A is a pseudo-involution if and only if A is an involution.

This paper deals with the groups formed by the products of in volutions and pseudo-involutions, the diagonalization of a group of involutions, and the construction of groups of involutions.