An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices

V. A. Baranskiĭ, Independence of lattices of congruences and groups of automorphisms of lattices, Izv. Vyssh. Uchebn. Zaved. Mat., 76:12 (1984), 12–17; English translation: Soviet Math. (Iz. VUZ), 28:12 (1984), 12–19 (in Russian).

G. Birkhoff, On groups of automorphisms, Revista Union Mat. Argentina, 11 (1946), 155–157 (in Spanish).

G. Czédli, Representing homomorphisms of distributive lattices as restrictions of congruences of rectangular lattices, Algebra Universalis, 67 (2012), 313–345.

G. Czédli, The ordered set of principal congruences of a countable lattice, Algebra Universalis, published online, doi: 10.1007/s00012-016-0376-1.

G. Czédli, Representing a monotone map by principal lattice congruences, Acta Math. Hungar., 147 (2015), 12–18; doi: 10.1007/s10474-015-0539-0.

G. Czédli, Large sets of lattices without order embeddings, Communications in Algebra, 44 (2016), 668–679.

G. Czédli, Representing some families of monotone maps by principal lattice congruences, Algebra Universalis, submitted; (Available at http://www.math.u-szeged.hu/~czedli/ as well as other papers of the author referenced in this paper.).

G. Czédli and M. Maróti, Two notes on the variety generated by planar modular lattices, Order, 26 (2009), 109–117.

R. Freese, The structure of modular lattices of width four with applications to varieties of lattices, Mem. Amer. Math. Soc., 9 (1977), no. 181.

R. Freese, J. Ježek and J. B. Nation, Free Lattices, Mathematical Surveys and Monographs 42, American Mathematical Society, Providence, RI, 1995.

R. Frucht, Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math., 6 (1939), 239–250 (in German).

R. Frucht, Graphs of degree three with a given abstract group, Canadian J. Math., 1 (1949), 365–378.

R. Frucht, Lattices with a given abstract group automorphisms, Canad. J. Math., 2 (1950), 417–419.

G. Grätzer, The Congruences of a Finite Lattice. A Proof-by-Picture Approach, Birkhäuser, Boston, 2006.

G. Grätzer, Lattice Theory: Foundation, Birkhäuser Verlag, Basel, 2011.

G. Grätzer, The order of principal congruences of a bounded lattice, Algebra Universalis, 70 (2013), 95–105.

G. Grätzer, Homomorphisms and principal congruences of bounded lattices, Acta Sci. Math. (Szeged), to appear; arXiv: 1507.03270.

G. Grätzer and H. Lakser, Homomorphisms of distributive lattices as restrictions of congruences. II. Planarity and automorphisms, Canadian J. Math., 46 (1994), 3–54.

G. Grätzer, H. Lakser and E. T. Schmidt, Congruence lattices of finite semimodular lattices, Canad. Math. Bull., 41 (1998), 290–297.

G. Grätzer and R. W. Quackenbush, Positive universal classes in locally finite varieties, Algebra Universalis, 64 (2010), 1–13.

G. Grätzer and E. T. Schmidt, The strong independence theorem for automorphism groups and congruence lattices of finite lattices, Beiträge Algebra Geom., 36 (1995), 97–108.

G. Grätzer and J. Sichler, On the endomorphism semigroup (and category) of bounded lattices, Pacific J. Math., 35 (1970), 639–647.

G. Grätzer and F. Wehrung, The strong independence theorem for automorphism groups and congruence lattices of arbitrary lattices, Adv. in Appl. Math., 24 (2000), 181–221.

J. de Groot, Groups represented by homeomorphism groups, Math. Ann., 138 (1959), 80–102.

G. Sabidussi, Graphs with given infinite group, Monatsh. Math., 64 (1960), 64–67.

A. Urquhart, A topological representation theory for lattices, Algebra Universalis, 8 (1978), 45–58.