| Popis: |
The basic mappings of affine plane A, considered here, are translations (elations with the axes at infinity) and reflections (involutory homologies with the center or the axes at infinity). We prove that these mappings preserve 'the square of the lenght' under the assumption char K different from 2. Additionally, we consider the group of isometries of the plane A placing emphasis on subgroup T°< h > (Frobenius group), where the normal subgroup T consists of translations of A and involution h is a reflection through the origin. As an illustration we show the group of isometries of affine plane A over K=GF(3). |
