Abstract. For a bounded lattice $L$, the principal congruences of $L$ form a bounded ordered set $\princ L$. G. Grätzer proved in 2013 that every bounded ordered set can be represented in this way. Also, G.Birkhoff proved in 1946 that every group is isomorphic to the group of automorphisms of an appropriate lattice. Here, for an arbitrary bounded ordered set $P$ with at least two elements and an arbitrary group $G$, we construct a selfdual lattice $L$ of length sixteen such that $\princ L$ is isomorphic to $P$ and the automorphism group of $L$ is isomorphic to $G$.

DOI: 10.14232/actasm-015-817-8

AMS Subject Classification (1991): 06B10

Keyword(s): principal congruence, lattice congruence, lattice automorphism, ordered set, bounded poset, quasi-colored lattice, preordering, quasiordering, monotone map, simultaneous representation, independence, automorphism group

Received September 6, 2015, and in revised form September 28, 2015. (Registered under 67/2015.)