| dc.description.abstract | The aim of this thesis is to examine some of the symmetries of the Klein quartic curve by describing the fixed points of the subgroups of its automorphism group, and some orbits of fixed points on the quartic curve and on the curves of the covariants. In chapter 2, we define the Klein quartic invariant and its covariants. In chapter 3, we describe generators and cyclic subgroups of the automorphism group of the Klein quartic curve, specifically the isomorphic groups the projective special linear group PSL(2,7) and the general linear group GL(3,2). Next, in chapter 4, we examine the representation of the automorphism group in GL(3,C) and the fixed points of its subgroups. Finally, in chapter 5, by way of examination of some fixed points on the curve of an invariant of degree 21, we show that specific products of the fixed lines of groups of order 2 return an integral factoring of the degree-21 invariant. | nob |