The automorphism group of the universal distributive lattice
by
Manfred Droste
Dresden University of Technology
Coauthors: Dugald Macpherson

A lattice L is called homogeneous, if each isomorphism between two finite sublattices of L extends to an automorphism of L. A lattice L is called universal, if each countable lattice can be embedded into L. It is known that up to isomorphism there is a unique countable universal homogeneous distributive lattice U. First we show that if L is any homogeneous distributive lattice (with more than 1 element), then L is isomorphic either to the chain Q of rationals or to U. Then we describe all normal subgroups of the automorphism group Aut(U). There are exactly 3 proper non-trivial ones: R(U) comprising all automorphisms fixing pointwise some ideal, L(U) containing all automorphisms fixing pointwise some filter, and the intersection B(U) = R(U) \cap L(U), which is simple. Thus Aut(U) and Aut(Q) have isomorphic normal subgroup lattices.

Date received: June 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-95.