Matrix forms for isometries of the affine plane AG(2, q) and of the corresponding Miquelian Mobius plane


We give the matrix form for the isometries of AG(2, q) and the corresponding Miquelian Mobius plane depending on the choice of an irreducible polynomial of second degree over GF(q). In particular we provide the above matrix form for the automorphisms of these planes preserving the set of the affine ellipses of AG(2,q).

DOI Code: 10.1285/i15900932v28n2p175

Keywords: finite affine plane; Miquelian M¨obius plane; squared length; squared distance; isometry

Classification: 05B25

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