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Automorphism groups of systems of equivalence and partial order relations. (English) Zbl 0814.20027

The paper deals with representations of groups and permutation groups by means of groups of automorphisms of binary relational systems. It is proved that each group can be represented as the group of automorphisms of an equivalence structure \((X,E)\) where \(\text{Aut}(X,E)\) has at most two orbits on \((X,E)\). Further the author shows that every permutation group is isomorphic to the group of semi-automorphisms of a system of well-order relations. Simultaneous representations of all subgroups of a group as automorphism groups of subsystems of a system of partial orders (or equivalences) are also given there.

MSC:

20F29 Representations of groups as automorphism groups of algebraic systems
20B27 Infinite automorphism groups
08A35 Automorphisms and endomorphisms of algebraic structures
20B10 Characterization theorems for permutation groups
06A06 Partial orders, general
08A30 Subalgebras, congruence relations
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