Isomorphism Universal Varieties of Heyting Algebras

M. E. Adams, V. Koubek, J. Sichler
1990 Transactions of the American Mathematical Society  
A variety V is group universal if every group G is isomorphic to the automorphism group Aut(A) of an algebra A E V; if, in addition, all finite groups are thus representable by finite algebras from V, the variety V is said to be finitely group universal. We show that finitely group universal varieties of Heyting algebras are exactly the varieties which are not generated by chains, and that a chain-generated variety V is group universal just when it contains a four-element chain. Furthermore, we
more » ... in. Furthermore, we show that a variety V of Heyting algebras is group universal whenever the cyclic group of order three occurs as the automorphism group of some A E V. The results are sharp in the sense that, for every group universal variety and for every group G, there is a proper class of pairwise nonisomorphic Heyting algebras A E V for which Aut(A) ~ G. Heyting algebra if (H; v, 1\, 0, 1) is a distributive (0, 1 )-lattice and -t is
doi:10.2307/2001347 fatcat:2eegqqmtize2di53c2g2zgsqvy