Symbolic incidence geometry proposal for doing geometry with a computer (Part 2 of 2)

We investigate geometric structures fulfilling certain symmetry conditions. Examples for such symmetry conditions are: • Require the existence of a non-trivial automorphism. • Require the existence of an automorphism of given order, for example of order 2. • Require the existence of an automorphism with a given structure of fixed points, for example a central collineation [26]. • Require the existence of an automorphism group with certain transitivity properties (2-transitive, primitive, etc.). • Require the existence of an automorphism group with a certain grouptheoretic structure. As an example we discuss the Theorem of Baer [2]: If a is an involutory automorphism of a projective plane P, then a is either a central collineation or its fix points form a Baer subptane of P. SIG will support proofs of theorems of this kind. In order to investigate the structure of the fixed points of an involution in P, the following facts play a crucial role:

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