Automorphisms of symmetric and double symmetric chain structures (Q844024)

The paper focuses on symmetric and double symmetric chain structures. A chain structure is a net \(({\mathcal P}, {\mathcal G}_1, {\mathcal G}_2)\) together with a set of chains \({\mathcal C}\) characterized by particular incidence axioms. Examples are webs, 2-structures, hyperbola structures or Minkowski planes. In a chain structure to each pair of chains a permutation on the point-set can be associated. If such a permutation maps chains of \({\mathcal C}\) onto chains of \({\mathcal C}\), then the chain structure is called double symmetric, or simply symmetric in case this property holds for reflexions only. In the paper the authors give a description of automorphism groups of symmetric and double symmetric chains and they discuss in detail the automorphism groups of double symmetric 1-, 2- and 3-structures.