Parametric 2-decompositions in complete linear groups of small order over the field - Shchedryk, V. (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 512.64We obtain a parametric decomposition of elements of complete linear groups of the second and third orders over an arbitrary field.  This decomposition is based on the canonical (unambiguous) representation of these elements in the form of the product of elements from the groups of commutators of certain Jordan matrices  and representatives of the left cosets of these groups.