Description of Projective Transvection of Projective Special Linear Group PSL2(K) Over a Field K. (June 2020)

• Record Type: Journal Article
• Authors: Sabbar, Shakir; Widodo, Agus; Hidayat, Noor; Alghofari, Abdul Rouf
• Is Part Of: Journal of physics. Volume 1562(2020)
• Publication Date: 2020-06
• Subjects: Physics -- Congresses; 530.5
• DOI: 10.1088/1742-6596/1562/1/012012
• Languages: English
• ISSNs: 1742-6588

Abstract

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 g Z 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.