The finite complete rewriting systems for matrix semigroups

The aim of this study is to consider some presentations for the semigroups of 2×2 matrices and all 2×2 matrices of determinant 0 or 1 over the field GF(p) (p:prime). We show that the matrix semigroups can be described by a finite complete rewriting systems as a consequence of which we obtain new presentations for matrix semigroups and we find the normal forms of these presentations. Moreover, we obtain an abelian group presentation for the second integral homology of special linear semigroups SLS(2,p).