Description of Projective Transvection of Projective Special Linear Group PSL 2(K) Over a Field K

Abstract

The purpose of this paper is to introduce one of the most important element closely connected with the classical linear group namely projective special linear groups SL 2(K)/Z of degree 2 over a field K, where Z is the center of the special linear group SL 2(K) consists of all scalar matrices whose determinants 1. This element called projective transvection which is an element of the projective special linear group PSL 2(K) that is, a coset gZ where g is some element in SL 2(K). In the present study, we will extend our conception about the projective transvection, so we can say this element is generating set of PSL 2(K). For that reason, we need todescribe this element for obtaining more conception about PSL 2(K) especially to describe subgroups of PSL 2(K) that have been generated by projective transvection.